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Journal articles on the topic 'Two-point BVP'

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Published: 5 June 2025

Last updated: 1 August 2025

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1

Kong, Xiangshan, and Haitao Li. "Solvability of a Class of Higher-Order Fractional Two-Point Boundary Value Problem." Chinese Journal of Mathematics 2014 (January 2, 2014): 1–5. http://dx.doi.org/10.1155/2014/871908.

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This paper investigates the solvability of a class of higher-order fractional two-point boundary value problem (BVP), and presents several new results. First, Green’s function of the considered BVP is obtained by using the property of Caputo derivative. Second, based on Schaefer’s fixed point theorem, the solvability of the considered BVP is studied, and a sufficient condition is presented for the existence of at least one solution. Finally, an illustrative example is given to support the obtained new results.

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2

El-Gamel, Mohamed, and Mahmoud Abd El Hady. "BERNOULLI COLLOCATION FOR SOLVING TWO-POINT BVP IN MODELLING VISCOELASTIC FLOWS." Matrix Science Mathematic 8, no. 1 (2024): 16–19. https://doi.org/10.26480/msmk.01.2024.16.19.

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Bernoulli bases are developed to approximate the solutions of two-point BVP in modelling viscoelastic flows in which the shifted Chebyshev collocation points are used as collocation nodes. Properties of Bernoulli bases are then used to reduce the two-point BVP in modelling viscoelastic flows to systems of nonlinear algebraic equations. The results show the agreement between the exact solutions and the approximate solutions. Form the numerical results we see that the proposed method gives accurate results.

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3

Liu, Bo, and Yansheng Liu. "Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space." Journal of Function Spaces and Applications 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/585639.

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This paper investigates the existence of positive solutions to a two-point boundary value problem (BVP) for singular fractional differential equations in Banach space and presents a number of new results. First, by constructing a novel cone and using the fixed point index theory, a sufficient condition is established for the existence of at least two positive solutions to the approximate problem of the considered singular BVP. Second, using Ascoli-Arzela theorem, a sufficient condition is obtained for the existence of at least two positive solutions to the considered singular BVP from the conv

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4

Kong, Xiangshan, and Haitao Li. "Positive Solutions to a Fractional-Order Two-Point Boundary Value Problem with p-Laplacian Operator." ISRN Mathematical Analysis 2013 (November 10, 2013): 1–12. http://dx.doi.org/10.1155/2013/898206.

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This paper systematically investigates positive solutions to a kind of two-point boundary value problem (BVP) for nonlinear fractional differential equations with p-Laplacian operator and presents a number of new results. First, the considered BVP is converted to an operator equation by using the property of the Caputo derivative. Second, based on the operator equation and some fixed point theorems, several sufficient conditions are presented for the nonexistence, the uniqueness, and the multiplicity of positive solutions. Finally, several illustrative examples are given to support the obtaine

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5

Anderson, Douglas R., and Christopher C. Tisdell. "Discrete Approaches to Continuous Boundary Value Problems: Existence and Convergence of Solutions." Abstract and Applied Analysis 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/3910972.

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We investigate two types of first-order, two-point boundary value problems (BVPs). Firstly, we study BVPs that involve nonlinear difference equations (the “discrete” BVP); and secondly, we study BVPs involving nonlinear ordinary differential equations (the “continuous” BVP). We formulate some sufficient conditions under which the discrete BVP will admit solutions. For this, our choice of methods involves a monotone iterative technique and the method of successive approximations (a.k.a. Picard iterations) in the absence of Lipschitz conditions. Our existence results for the discrete BVP are of

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6

TSUMOTO, K., T. YOSHINAGA, and H. KAWAKAMI. "BIFURCATIONS IN SYNAPTICALLY COUPLED BVP NEURONS." International Journal of Bifurcation and Chaos 11, no. 04 (2001): 1053–64. http://dx.doi.org/10.1142/s0218127401002651.

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We investigate bifurcations of periodic solutions in model equations of two and three Bonhöffer–van der Pol (BVP) neurons coupled through the characteristics of synaptic transmissions with a time delay. Bifurcations of the coupled BVP neurons are compared with bifurcations of synaptically coupled Hodgkin–Huxley neurons. We obtained a parameter set of the BVP system, such that the two systems are qualitatively very similar from a bifurcational point of view. This study is a base for the analysis of synaptically coupled neurons with a large number of coupling strategies.

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7

Zhang, Wei, and Jinbo Ni. "New sharp estimates of the interval length of the uniqueness results for several two-point fractional boundary value problems." Electronic Research Archive 31, no. 3 (2023): 1253–70. http://dx.doi.org/10.3934/era.2023064.

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<abstract><p>This paper investigates the existence and uniqueness of solutions for several two-point fractional BVPs, including hybrid fractional BVP, sequential fractional BVP and so on. Using the Banach contraction mapping theorem, some sharp conditions that depend on the length of the given interval are presented, which ensure the uniqueness of solutions for the considered BVPs. Illustrative examples are also constructed. The results obtained in this study are noteworthy extensions of earlier works.</p></abstract>

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8

Li, Ning, Haibo Gu, and Yiru Chen. "BVP for Hadamard Sequential Fractional Hybrid Differential Inclusions." Journal of Function Spaces 2022 (February 24, 2022): 1–27. http://dx.doi.org/10.1155/2022/4042483.

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The study is concerned with the Hadamard sequential fractional hybrid differential inclusions with two-point hybrid integral boundary conditions. With the help of the Dhage fixed-point theorem for the product of two operators and the Covitz-Nadler fixed-point theorem in the case of fractional inclusions, we obtain the existence results of solutions for Hadamard sequential fractional hybrid differential inclusions. Finally, two examples are presented to illustrate the main results.

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9

Ramachandra, L. S., and D. Roy. "A New Method for Nonlinear Two-Point Boundary Value Problems in Solid Mechanics." Journal of Applied Mechanics 68, no. 5 (2001): 776–86. http://dx.doi.org/10.1115/1.1387444.

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A local and conditional linearization of vector fields, referred to as locally transversal linearization (LTL), is developed for accurately solving nonlinear and/or nonintegrable boundary value problems governed by ordinary differential equations. The locally linearized vector field is such that solution manifolds of the linearized equation transversally intersect those of the nonlinear BVP at a set of chosen points along the axis of the only independent variable. Within the framework of the LTL method, a BVP is treated as a constrained dynamical system, which in turn is posed as an initial va

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10

Guo, Dajun. "Nonnegative solutions of two-point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces." Journal of Applied Mathematics and Stochastic Analysis 4, no. 1 (1991): 47–69. http://dx.doi.org/10.1155/s1048953391000035.

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In this paper, we combine the fixed point theory, fixed point index theory and cone theory to investigate the nonnegative solutions of two-point BVP for nonlinear second order integrodifferential equations in Banach spaces. As application, we get some results for the third order case. Finally, we give several examples for both infinite and finite systems of ordinary nonlinear integrodifferential equations.

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11

BAKRI, TAOUFIK, YURI A. KUZNETSOV, FERDINAND VERHULST, and EUSEBIUS DOEDEL. "MULTIPLE SOLUTIONS OF A GENERALIZED SINGULAR PERTURBED BRATU PROBLEM." International Journal of Bifurcation and Chaos 22, no. 04 (2012): 1250095. http://dx.doi.org/10.1142/s0218127412500952.

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Nonlinear two-point boundary value problems (BVPs) may have none or more than one solution. For the singularly perturbed two-point BVP εu″ + 2u′ + f(u) = 0, 0 < x < 1, u(0) = 0, u(1) = 0, a condition is given to have one and only one solution; also cases of more solutions have been analyzed. After attention to the form and validity of the corresponding asymptotic expansions, partially based on slow manifold theory, we reconsider the BVP within the framework of small and large values of the parameter. In the case of a special nonlinearity, numerical bifurcation patterns are studied that i

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12

Mkharrib, Haider A., Ahmed Hameed Kamil, Tahrier Nasser Salem, and Thekra H. Dahees. "A new homotopy analysis method analytical for singular two-point BVP solv." Journal of Interdisciplinary Mathematics 28, no. 1 (2025): 133–40. https://doi.org/10.47974/jim-1803.

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The purpose of this article is to introduce a new modification of the homotopy analytic method (HAM) to find an approximate or exact solution to the problem. The results show that this proposed modification is highly effective compared to the first iteration basic symmetric analysis method (HAM), whose solution is correct in most cases. Here are some examples to illustrate the proposed strategy

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13

Singh, Jitender. "A Nonlinear Shooting Method and Its Application to Nonlinear Rayleigh-Bénard Convection." ISRN Mathematical Physics 2013 (August 22, 2013): 1–9. http://dx.doi.org/10.1155/2013/650208.

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The simple shooting method is revisited in order to solve nonlinear two-point BVP numerically. The BVP of the type is considered where components of are known at one of the boundaries and components of are specified at the other boundary. The map is assumed to be smooth and satisfies the Lipschitz condition. The two-point BVP is transformed into a system of nonlinear algebraic equations in several variables which, is solved numerically using the Newton method. Unlike the one-dimensional case, the Newton method does not always have quadratic convergence in general. However, we prove that the ra

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14

Yu, Zhan Dong, Jiang Tao Xu, and Xian Feng Wang. "Position and Anti-Swing Control Based on BVP Arithmetic for Bridge Cranes." Advanced Materials Research 287-290 (July 2011): 3102–5. http://dx.doi.org/10.4028/www.scientific.net/amr.287-290.3102.

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The anti-swing problem of the bridge cranes is discussed. The position and anti-swing control strategy based on BVP arithmetic is presented. The position and anti-swing control programming of bridge cranes can be transformed into the two-point boundary value problem (BVP) of nonlinear systems. According to the boundary conditions, the tractive force function of Fourier series form with free parameters is constructed. The BVP is solved with the bvp4c function in Matlab toolbox, and the tractive force sequence is obtained. The presented position and anti-swing control strategy for bridge cranes

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15

Mohammed, Nedal, Laman R. Sultan, and Santosh Lomte. "Privacy preserving outsourcing algorithm for two-point linear boundary value problems." Indonesian Journal of Electrical Engineering and Computer Science 16, no. 2 (2019): 1065. http://dx.doi.org/10.11591/ijeecs.v16.i2.pp1065-1069.

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<p>One of a powerful application in the age of cloud computing is the outsourcing of scientific computations to cloud computing which makes cloud computing a very powerful computing paradigm, where the customers with limited computing resource and storage devices can outsource the sophisticated computation workloads into powerful service providers. One of scientific computations problem is Two-Point Boundary Value Problems(BVP) is a basic engineering and scientific problem, which has application in various domains. In this paper, we propose a privacy-preserving, verifiable and efficient

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16

Gil’, Michael I. "Positivity conditions and bounds for Green’s functions for higher order two-point BVP." Central European Journal of Mathematics 9, no. 5 (2011): 1156–63. http://dx.doi.org/10.2478/s11533-011-0052-9.

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17

Mukhigulashvili, Sulkhan, and Mariam Manjikashvili. "On one two-point BVP for the fourth order linear ordinary differential equation." Georgian Mathematical Journal 24, no. 2 (2017): 265–75. http://dx.doi.org/10.1515/gmj-2016-0077.

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AbstractIn this article we consider the two-point boundary value problem\left\{\begin{aligned} &\displaystyle u^{(4)}(t)=p(t)u(t)+h(t)\quad\text{for }% a\leq t\leq b,\\ &\displaystyle u^{(i)}(a)=c_{1i},\quad u^{(i)}(b)=c_{2i}\quad(i=0,1),\end{% aligned}\right.where {c_{1i},c_{2i}\in R}, {h,p\in L([a,b];R)}. Here we study the question of dimension of the space of nonzero solutions and oscillatory behaviors of nonzero solutions on the interval {[a,b]} for the corresponding homogeneous problem, and establish efficient sufficient conditions of solvability for the nonhomogeneous problem.

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18

Yu, Zhan Dong, and Xian Feng Wang. "Swing-Up Control by BVP Arithmetic for the Rotational Inverted Pendulum." Advanced Materials Research 211-212 (February 2011): 515–19. http://dx.doi.org/10.4028/www.scientific.net/amr.211-212.515.

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The swing-up control strategy via BVP arithmetic is presented for rotational inverted pendulum. The swing-up control programming from hanging to the upright position can be transformed into the two-point boundary value problem (BVP) of nonlinear systems. According to the boundary conditions of the swing-up process, the control torque function of Fourier series form with free parameters is constructed. The BVP is solved with the bvp4c function in Matlab toolbox, and the control torque sequence is obtained. The swing-up process is open-loop feedforward control essentially. In order to inhibition

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19

Sadyrbaev, Felix. "Multiplicity of Solutions for Second Order Two-Point Boundary Value Problems with Asymptotically Asymmetric Nonlinearities at Resonance." gmj 14, no. 2 (2007): 351–60. http://dx.doi.org/10.1515/gmj.2007.351.

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Abstract Estimations of the number of solutions are given for various resonant cases of the boundary value problem 𝑥″ + 𝑔(𝑡, 𝑥) = 𝑓(𝑡, 𝑥, 𝑥′), 𝑥(𝑎) cos α – 𝑥′(𝑎) sin α = 0, 𝑥(𝑏) cos β – 𝑥′(𝑏) sin β = 0, where 𝑔(𝑡, 𝑥) is an asymptotically linear nonlinearity, and 𝑓 is a sublinear one. We assume that there exists at least one solution to the BVP.

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20

LIU, YUJI. "SOLVABILITY OF NEUMANN TYPE NON-HOMOGENEOUS MULTI-POINT BVP FOR SECOND ORDER DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN." Analysis and Applications 07, no. 03 (2009): 279–95. http://dx.doi.org/10.1142/s0219530509001402.

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We consider the following multi-point boundary value problems [Formula: see text] New sufficient conditions to guarantee the existence of at least one solution of the above mentioned BVP are established. Two examples are presented to illustrate the main result.

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21

CAMPOS, RAFAEL G., and RAFAEL GARCÍA RUIZ. "FAST INTEGRATION OF ONE-DIMENSIONAL BOUNDARY VALUE PROBLEMS." International Journal of Modern Physics C 24, no. 11 (2013): 1350082. http://dx.doi.org/10.1142/s0129183113500824.

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Two-point nonlinear boundary value problems (BVPs) in both unbounded and bounded domains are solved in this paper using fast numerical antiderivatives and derivatives of functions of L2(-∞, ∞). This differintegral scheme uses a new algorithm to compute the Fourier transform. As examples we solve a fourth-order two-point boundary value problem (BVP) and compute the shape of the soliton solutions of a one-dimensional generalized Korteweg–de Vries (KdV) equation.

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22

Filipowska, Renata. "The Iterative Shooting Method Applied to the Modeling of the In-Run Profile of a Ski Jumping Hill." Applied Mechanics and Materials 712 (January 2015): 37–42. http://dx.doi.org/10.4028/www.scientific.net/amm.712.37.

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This paper treats an iterative shooting method based on sensitivity functions for solving non–linear two–point boundary value problems (BVPs), in the form of a second–order differential equation and four boundary conditions. The solution of this BVP constitutes an in–run profile of a ski jumping hill. It is characterized by reduced a normal reaction force, which has impact on ski jumper’s legs during sliding downhill. In order to use this method, it is necessary to convert the BVP to an appropriate initial value problem (IVP). Consequently, in each iteration, we must solve a system of six firs

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23

El-Gamel, Mohamed, Ola Mohamed, and Neveen El-Shamy. "A Robust and Effective Method for Solving Two-Point BVP in Modelling Viscoelastic Flows." Applied Mathematics 11, no. 01 (2020): 23–34. http://dx.doi.org/10.4236/am.2020.111003.

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24

Yaseen, Muhammad, Sadia Mumtaz, Reny George, and Azhar Hussain. "Existence Results for the Solution of the Hybrid Caputo–Hadamard Fractional Differential Problems Using Dhage’s Approach." Fractal and Fractional 6, no. 1 (2021): 17. http://dx.doi.org/10.3390/fractalfract6010017.

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In this work, we explore the existence results for the hybrid Caputo–Hadamard fractional boundary value problem (CH-FBVP). The inclusion version of the proposed BVP with a three-point hybrid Caputo–Hadamard terminal conditions is also considered and the related existence results are provided. To achieve these goals, we utilize the well-known fixed point theorems attributed to Dhage for both BVPs. Moreover, we present two numerical examples to validate our analytical findings.

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25

Omaba, McSylvester Ejighikeme, and Louis O. Omenyi. "Boundary value problems for a class of stochastic nonlinear fractional order differential equations." Open Journal of Mathematical Analysis 4, no. 2 (2020): 152–59. http://dx.doi.org/10.30538/psrp-oma2020.0074.

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Consider a class of two-point Boundary Value Problems (BVP) for a stochastic nonlinear fractional order differential equation \(D^\alpha u(t)=\lambda\sqrt{I^\beta[\sigma^2(t,u(t))]}\dot{w}(t)\ ,0< t< 1\) with boundary conditions \(u(0)=0,\,\,u'(0)=u'(1)=0,\) where \(\lambda>0\) is a level of the noise term, \(\sigma:[0,1]\times\mathbb{R}\rightarrow\mathbb{R}\) is continuous, \(\dot{w}(t)\) is a generalized derivative of Wiener process (Gaussian white noise), \(D^\alpha\) is the Riemann-Liouville fractional differential operator of order \(\alpha\in (3,4)\) and \(I^\beta,\,\,\beta>0

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26

Omaba, McSylvester Ejighikeme, and Louis O. Omenyi. "Boundary value problems for a class of stochastic nonlinear fractional order differential equations." Open Journal of Mathematical Analysis 4, no. 2 (2020): 152–59. http://dx.doi.org/10.30538/psrp-oma2020.0074.

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Consider a class of two-point Boundary Value Problems (BVP) for a stochastic nonlinear fractional order differential equation \(D^\alpha u(t)=\lambda\sqrt{I^\beta[\sigma^2(t,u(t))]}\dot{w}(t)\ ,0< t< 1\) with boundary conditions \(u(0)=0,\,\,u'(0)=u'(1)=0,\) where \(\lambda>0\) is a level of the noise term, \(\sigma:[0,1]\times\mathbb{R}\rightarrow\mathbb{R}\) is continuous, \(\dot{w}(t)\) is a generalized derivative of Wiener process (Gaussian white noise), \(D^\alpha\) is the Riemann-Liouville fractional differential operator of order \(\alpha\in (3,4)\) and \(I^\beta,\,\,\beta>0

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27

Souid, Mohammed Said, Ahmed Refice, and Kanokwan Sitthithakerngkiet. "Stability of p(·)-Integrable Solutions for Fractional Boundary Value Problem via Piecewise Constant Functions." Fractal and Fractional 7, no. 2 (2023): 198. http://dx.doi.org/10.3390/fractalfract7020198.

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The goal of this work is to study a multi-term boundary value problem (BVP) for fractional differential equations in the variable exponent Lebesgue space (Lp(·)). Both the existence, uniqueness, and the stability in the sense of Ulam–Hyers are established. Our results are obtained using two fixed-point theorems, then illustrating the results with a comprehensive example.

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28

Anandaram, M. N. "Evaluation of Scipy.ode Integrators in Solving the Lane-Emden Equation for Polytropes as a Boundary Value Problem with a Fitting Method." Mapana - Journal of Sciences 16, no. 1 (2017): 67–80. http://dx.doi.org/10.12723/mjs.40.5.

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The use of Scipy integrators like dopri5 and others in accurately solving the Lane-Emden equation of a polytrope as a two-point BVP with fitting is investigated by comparing the Emden radius with the extended precision reference value obtained by Boyd's Chebyshev spectral method. It is found that both dopri5 and dop853 integrators provide acceptable accuracy upto 14 decimal digits.

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29

Agarwal, R. P., and I. Kiguradze. "Two-point boundary value problems for higher-order linear differential equations with strong singularities." Boundary Value Problems 2006 (2006): 1–32. http://dx.doi.org/10.1155/bvp/2006/83910.

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30

Gao, Li-Juan, and Jian-Ping Sun. "Positive Solutions of a Third-Order Three-Point BVP with Sign-Changing Green’s Function." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/406815.

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We are concerned with the following third-order three-point boundary value problem:u′′′t=ft, ut, t∈0, 1, u′0=u1=0and u′′η-αu′1=0,whereα∈0, 1andη∈(14+α)/(24-3α),1. Although the corresponding Green’s function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions onfby using the two-fixed-point theorem due to Avery and Henderson.

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31

Zhao, Kaihong. "Solvability, Approximation and Stability of Periodic Boundary Value Problem for a Nonlinear Hadamard Fractional Differential Equation with p-Laplacian." Axioms 12, no. 8 (2023): 733. http://dx.doi.org/10.3390/axioms12080733.

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The fractional order p-Laplacian differential equation model is a powerful tool for describing turbulent problems in porous viscoelastic media. The study of such models helps to reveal the dynamic behavior of turbulence. Therefore, this article is mainly concerned with the periodic boundary value problem (BVP) for a class of nonlinear Hadamard fractional differential equation with p-Laplacian operator. By virtue of an important fixed point theorem on a complete metric space with two distances, we study the solvability and approximation of this BVP. Based on nonlinear analysis methods, we furth

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32

Almalahi, Mohammed A., Satish K. Panchal та Fahd Jarad. "Multipoint BVP for the Langevin Equation under φ -Hilfer Fractional Operator". Journal of Function Spaces 2022 (14 травня 2022): 1–14. http://dx.doi.org/10.1155/2022/2798514.

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In this research paper, we consider a class of boundary value problems for a nonlinear Langevin equation involving two generalized Hilfer fractional derivatives supplemented with nonlocal integral and infinite-point boundary conditions. At first, we derive the equivalent solution to the proposed problem at hand by relying on the results and properties of the generalized fractional calculus. Next, we investigate and develop sufficient conditions for the existence and uniqueness of solutions by means of semigroups of operator approach and the Krasnoselskii fixed point theorems as well as Banach

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33

Yao, Qing-liu. "Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative." Journal of Zhejiang University SCIENCE 5, no. 3 (2004): 353–57. http://dx.doi.org/10.1631/jzus.2004.0353.

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Qing-liu, Yao. "Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative." Journal of Zhejiang University-SCIENCE A 5, no. 3 (2004): 353–57. http://dx.doi.org/10.1631/bf02841022.

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35

Benzenati, Lyna, Svetlin Georgiev Georgiev, and Karima Mebarki. "Existence of positive solutions for a class of BVPs in Banach spaces." Studia Universitatis Babes-Bolyai Matematica 66, no. 4 (2021): 723–38. http://dx.doi.org/10.24193/subbmath.2021.4.10.

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In this work, we use index xed point theory for perturbation of expan- sive mappings by l-set contractions to study the existence of bounded positive solutions for a class of two-point boundary value problem (BVP) associated to second-order nonlinear di erential equation on the positive half-line. The nonlin- earity, which may exhibit a singularity at the origin, is written as a sum of two functions which behave di erently. These functions, depend on the solution and its derivative, take values in a general Banach space and have at most polynomial growth. An example to illustrate the main resu

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36

Raza, Ali, Mujahid Abbas, Hasanen A. Hammad, and Manuel De la Sen. "Fixed Point Approaches for Multi-Valued Prešić Multi-Step Iterative Mappings with Applications." Symmetry 15, no. 3 (2023): 686. http://dx.doi.org/10.3390/sym15030686.

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The purpose of this paper is to present some fixed point approaches for multi-valued Prešić k-step iterative-type mappings on a metric space. Furthermore, some corollaries are obtained to unify and extend many symmetrical results in the literature. Moreover, two examples are provided to support the main result. Ultimately, as potential applications, some contributions of integral type are investigated and the existence of a solution to the second-order boundary value problem (BVP) is presented.

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37

Zhang, Yixin, and Yujun Cui. "Positive Solutions for Two-Point Boundary Value Problems for Fourth-Order Differential Equations with Fully Nonlinear Terms." Mathematical Problems in Engineering 2020 (November 6, 2020): 1–7. http://dx.doi.org/10.1155/2020/8813287.

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In this paper, we consider the existence of positive solutions for the fully fourth-order boundary value problem u 4 t = f t , u t , u ′ t , u ″ t , u ‴ t , 0 ≤ t ≤ 1 , u 0 = u 1 = u ″ 0 = u ″ 1 = 0 , where f : 0,1 × 0 , + ∞ × − ∞ , + ∞ × − ∞ , 0 × − ∞ , + ∞ ⟶ 0 , + ∞ is continuous. This equation can simulate the deformation of an elastic beam simply supported at both ends in a balanced state. By using the fixed-point index theory and the cone theory, we discuss the existence of positive solutions of the fully fourth-order boundary value problem. We transform the fourth-order differential equa

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38

Bouazza, Zoubida, Sina Etemad, Mohammed Said Souid, Shahram Rezapour, Francisco Martínez, and Mohammed K. A. Kaabar. "A Study on the Solutions of a Multiterm FBVP of Variable Order." Journal of Function Spaces 2021 (May 22, 2021): 1–9. http://dx.doi.org/10.1155/2021/9939147.

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In the present research study, for a given multiterm boundary value problem (BVP) involving the nonlinear fractional differential equation (NnLFDEq) of variable order, the uniqueness-existence properties are analyzed. To arrive at such an aim, we first investigate some specifications of this kind of variable order operator and then derive required criteria confirming the existence of solution. All results in this study are established with the help of two fixed-point theorems and examined by a practical example.

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39

Alomari, A. K., N. Ratib Anakira, A. Sami Bataineh, and I. Hashim. "Approximate Solution of Nonlinear System of BVP Arising in Fluid Flow Problem." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/136043.

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We extend for the first time the applicability of the Optimal Homotopy Asymptotic Method (OHAM) to find approximate solution of a system of two-point boundary-value problems (BVPs). The OHAM provides us with a very simple way to control and adjust the convergence of the series solution using the auxiliary constants which are optimally determined. Comparisons made show the effectiveness and reliability of the method.

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Singh, Prem. "New cubic b-spline origination and procedure of newton TAGE technique for reason of two-point BVP." International Journal of Statistics and Applied Mathematics 7, no. 2 (2022): 34–40. http://dx.doi.org/10.22271/maths.2022.v7.i2a.792.

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Ozana, S., and M. Schlegel. "Computation of Reference Trajectories for Inverted Pendulum with the Use of Two-point BvP with Free Parameters." IFAC-PapersOnLine 51, no. 6 (2018): 408–13. http://dx.doi.org/10.1016/j.ifacol.2018.07.119.

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Xiong, Feng. "Infinitely Many Solutions for a Perturbed Partial Discrete Dirichlet Problem Involving ϕc-Laplacian". Axioms 12, № 10 (2023): 909. http://dx.doi.org/10.3390/axioms12100909.

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In this paper, by using critical point theory, the existence of infinitely many small solutions for a perturbed partial discrete Dirichlet problems including the mean curvature operator is investigated. Moreover, the present study first attempts to address discrete Dirichlet problems with ϕc-Laplacian operator in relative to some relative existing references. Based on our knowledge, this is the research of perturbed partial discrete bvp with ϕc-Laplacian operator for the first time. At last, two examples are used to examplify the results.

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Alzahrani, K. A., N. A. Alzaid, H. O. Bakodah, and M. H. Almazmumy. "Computational Approach to Third-Order Nonlinear Boundary Value Problems via Efficient Decomposition Shooting Method." Axioms 13, no. 4 (2024): 248. http://dx.doi.org/10.3390/axioms13040248.

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The present manuscript proposes a computational approach to efficiently tackle a class of two-point boundary value problems that features third-order nonlinear ordinary differential equations. Specifically, this approach is based upon a combination of the shooting method with a modification of the renowned Adomian decomposition method. The approach starts by transforming the governing BVP into two appropriate initial-value problems, and thereafter, solves the resulting IVPs recurrently. In addition, the application of this method to varied test models remains feasible—of course, this is suppor

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Filipowska, Renata. "An Iterative Shooting Method for the Solution of Higher Order Boundary Value Problems with Additional Boundary Conditions." Solid State Phenomena 235 (July 2015): 31–36. http://dx.doi.org/10.4028/www.scientific.net/ssp.235.31.

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This paper treats an iterative shooting method based on sensitivity functions for solving non–linear two–point boundary value problems (BVPs), in the form of a fourth–order differential equation and more than four boundary conditions. The solution of this problem is possible only when the equation includes the required number of unknown parameters. In order to use this method, it is necessary to convert the BVP to an appropriate initial value problem (IVP). The presented method has been illustrated with a numerical example.

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Feckan, Michal, and Kateryna Marynets. "Non-local fractional boundary value problems with applications to predator-prey models." Electronic Journal of Differential Equations 2023, no. 01-?? (2023): 58. http://dx.doi.org/10.58997/ejde.2023.58.

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We study a nonlinear fractional boundary value problem (BVP) subject to non-local multipoint boundary conditions. By introducing an appropriate parametrization technique we reduce the original problem to an equivalent one with already two-point restrictions. Using a notion of Chebyshev nodes and Lagrange polynomials we construct a successive iteration scheme, that converges to the exact solution of the non-local problem for particular values of the unknown parameters, which are calculated numerically. For mote information see https://ejde.math.txstate.edu/Volumes/2023/58/abstr.html

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Benkerrouche, Amar, Mohammed Said Souid, Gani Stamov, and Ivanka Stamova. "Multiterm Impulsive Caputo–Hadamard Type Differential Equations of Fractional Variable Order." Axioms 11, no. 11 (2022): 634. http://dx.doi.org/10.3390/axioms11110634.

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In this study, we deal with an impulsive boundary value problem (BVP) for differential equations of variable fractional order involving the Caputo–Hadamard fractional derivative. The fundamental problems of existence and uniqueness of solutions are studied, and new existence and uniqueness results are established in the form of two fixed point theorems. In addition, Ulam–Hyers stability sufficient conditions are proved illustrating the suitability of the derived fundamental results. The obtained results are supported also by an example. Finally, the conclusion notes are highlighted.

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Islam, Sheikh Md. Rabiul. "Solve Boundary Value Problem of Shooting and Finite Difference Method Using Matlab." DIU Journal of Science & Technology 7, no. 2 (2024): 18–23. https://doi.org/10.5281/zenodo.13739252.

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In this paper, the order of convergence of finite difference methods& shooting method has been presented for the numerical solution of a two-point boundary value problem (BVP) with the second order difierential equations (ODE ’s) and analyzed. Suflicient condition guaranteeing a unique solution of the corresponding boundary value problem is also given. Numerical results are tabulated for typical numerical examples and compared with the shooting technique employing the classical Euler and fourth- order Runge-Kutta method using MATLAB 7.6. 0( R2008a).

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Ahmadini, Abdullah Ali H., Mahammad Khuddush, and Sabbavarapu Nageswara Rao. "Multiple Positive Solutions for a System of Fractional Order BVP with p-Laplacian Operators and Parameters." Axioms 12, no. 10 (2023): 974. http://dx.doi.org/10.3390/axioms12100974.

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In this paper, we investigate the existence of positive solutions to a system of fractional differential equations that include the (r1,r2,r3)-Laplacian operator, three-point boundary conditions, and various fractional derivatives. We use a combination of techniques, including cone expansion and compression of the functional type, and the Leggett–Williams fixed point theorem, to prove the existence of positive solutions. Finally, we provide two examples to illustrate our main results.

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Altuzarra, Oscar, David Manuel Solanillas, Enrique Amezua, and Victor Petuya. "Path Analysis for Hybrid Rigid–Flexible Mechanisms." Mathematics 9, no. 16 (2021): 1869. http://dx.doi.org/10.3390/math9161869.

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Hybrid rigid–flexible mechanisms are a type of compliant mechanism that combines rigid and flexible elements, being that their mobility is due to rigid-body joints and the relative flexibility of bendable rods. Two of the modeling methods of flexible rods are the Cosserat rod model and its simplification, the Kirchhoff rod model. Both of them present a system of differential equations that must be solved in conjunction with the boundary constraints of the rod, leading to a boundary value problem (BVP). In this work, two methods to solve this BVP are applied to analyze the influence of external

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Kazem, Saeed, Jamal Amani Rad, Kourosh Parand, and Saied Abbasbandy. "A New Method for Solving Steady Flow of a Third-Grade Fluid in a Porous Half Space Based on Radial Basis Functions." Zeitschrift für Naturforschung A 66, no. 10-11 (2011): 591–98. http://dx.doi.org/10.5560/zna.2011-0014.

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In this study, flow of a third-grade non-Newtonian fluid in a porous half space has been considered. This problem is a nonlinear two-point boundary value problem (BVP) on semi-infinite interval. We find the simple solutions by using collocation points over the almost whole domain [0;∞). Our method based on radial basis functions (RBFs) which are positive definite functions. We applied this method through the integration process on the infinity boundary value and simply satisfy this condition by Gaussian, inverse quadric, and secant hyperbolic RBFs.We compare the results with solution of other

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