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Journal articles on the topic 'Conjugate boundary value problems'

Author: Grafiati

Published: 14 March 2023

Last updated: 31 July 2025

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1

Agarwal, R. P., and D. O'Regan. "Discrete conjugate boundary value problems." Applied Mathematics Letters 13, no. 2 (2000): 97–104. http://dx.doi.org/10.1016/s0893-9659(99)00171-8.

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2

Li, Weifeng, and Jinyuan Du. "Linear conjugate boundary value problems." Wuhan University Journal of Natural Sciences 12, no. 6 (2007): 985–91. http://dx.doi.org/10.1007/s11859-007-0037-5.

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3

Chuan-Rong, Wang, and Yang Qiao-Lin. "Linear conjugate boundary value problems." Complex Variables, Theory and Application: An International Journal 31, no. 2 (1996): 105–19. http://dx.doi.org/10.1080/17476939608814952.

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4

Palamides, P. K. "Conjugate boundary value problems, via Sperner's lemma." Nonlinear Analysis: Theory, Methods & Applications 46, no. 2 (2001): 299–308. http://dx.doi.org/10.1016/s0362-546x(00)00124-3.

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5

Wong, P. J. Y. "Triple positive solutions of conjugate boundary value problems." Computers & Mathematics with Applications 36, no. 9 (1998): 19–35. http://dx.doi.org/10.1016/s0898-1221(98)00190-4.

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6

Agarwal, Ravi P., Martin Bohner, and Patricia J. Y. Wong. "Positive solutions and eigenvalues of conjugate boundary value problems." Proceedings of the Edinburgh Mathematical Society 42, no. 2 (1999): 349–74. http://dx.doi.org/10.1017/s0013091500020307.

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We consider the following boundary value problemwhere λ > 0 and 1 ≤ p ≤ n – 1 is fixed. The values of λ are characterized so that the boundary value problem has a positive solution. Further, for the case λ = 1 we offer criteria for the existence of two positive solutions of the boundary value problem. Upper and lower bounds for these positive solutions are also established for special cases. Several examples are included to dwell upon the importance of the results obtained.

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7

McLachlan, Robert I., and Christian Offen. "Hamiltonian Boundary Value Problems, Conformal Symplectic Symmetries, and Conjugate Loci." New Zealand Journal of Mathematics 48 (December 31, 2018): 83–99. http://dx.doi.org/10.53733/34.

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In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and ordinary and reversal phase space symmetries have been considered. Here we present a convenient, coordinate free framework to analyse separated Lagrangian boundary value problems which include classical Dirichlet, Neumann and Robin boundary value problems. The framework is then used to prove the existence of obstructions arising from conformal symplectic sy

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8

Wong, Patricia J. Y., and Ravi P. Agarwal. "Multiple Solutions of Generalized Multipoint Conjugate Boundary Value Problems." gmj 6, no. 6 (1999): 567–90. http://dx.doi.org/10.1515/gmj.1999.567.

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Abstract We consider the boundary value problem 𝑦(𝑛) (𝑡) = 𝑃(𝑡, 𝑦), 𝑡 ∈ (0, 1) 𝑦(𝑗) (𝑡𝑖) = 0, 𝑗 = 0, . . . , 𝑛𝑖 – 1, 𝑖 = 1, . . . , 𝑟, where 𝑟 ≥ 2, 𝑛𝑖 ≥ 1 for 𝑖 = 1, . . . , 𝑟, and 0 = 𝑡1 < 𝑡2 < ⋯ < 𝑡𝑟 = 1. Criteria are offered for the existence of double and triple ‘positive’ (in some sense) solutions of the boundary value problem. Further investigation on the upper and lower bounds for the norms of these solutions is carried out for special cases. We also include several examples to illustrate the importance of the results obtained.

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9

Davis, John M., Paul W. Eloe, and Johnny Henderson. "Triple Positive Solutions for Multipoint Conjugate Boundary Value Problems." gmj 6, no. 5 (1999): 415–20. http://dx.doi.org/10.1515/gmj.1999.415.

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Abstract For the 𝑛th order nonlinear differential equation 𝑦(𝑛)(𝑡) = 𝑓(𝑦(𝑡)), 𝑡 ∈ [0, 1], satisfying the multipoint conjugate boundary conditions, 𝑦(𝑗)(𝑎𝑖) = 0, 1 ≤ 𝑖 ≤ 𝑘, 0 ≤ 𝑗 ≤ 𝑛𝑖 – 1, 0 = 𝑎1 < 𝑎2 < ⋯ < 𝑎𝑘 = 1, and , where 𝑓 : ℝ → [0, ∞) is continuous, growth condtions are imposed on 𝑓 which yield the existence of at least three solutions that belong to a cone.

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10

Kaufmann, Eric R., and Nickolai Kosmatov†. "Singular Conjugate Boundary Value Problems on a Time Scale." Journal of Difference Equations and Applications 10, no. 2 (2004): 119–27. http://dx.doi.org/10.1080/1023619031000114332.

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11

Wong, Patricia J. Y., and Ravi P. Agarwal. "Eigenvalue theorems for discrete multipoint conjugate boundary value problems." Journal of Computational and Applied Mathematics 113, no. 1-2 (2000): 227–40. http://dx.doi.org/10.1016/s0377-0427(99)00258-7.

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12

Wong, P. J. Y. "Triple positive solutions of conjugate boundary value problems II." Computers & Mathematics with Applications 40, no. 4-5 (2000): 537–57. http://dx.doi.org/10.1016/s0898-1221(00)00178-4.

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13

Webb, J. R. L. "Nonlocal conjugate type boundary value problems of higher order." Nonlinear Analysis: Theory, Methods & Applications 71, no. 5-6 (2009): 1933–40. http://dx.doi.org/10.1016/j.na.2009.01.033.

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14

Agarwal, R. P., M. Bohner, and P. J. Y. Wong. "Eigenvalues and eigenfunctions of discrete conjugate boundary value problems." Computers & Mathematics with Applications 38, no. 3-4 (1999): 159–83. http://dx.doi.org/10.1016/s0898-1221(99)00192-3.

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15

Eloe, Paul W., and Johnny Henderson. "Singular Nonlinear (k, n−k) Conjugate Boundary Value Problems." Journal of Differential Equations 133, no. 1 (1997): 136–51. http://dx.doi.org/10.1006/jdeq.1996.3207.

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16

Yao, Qingliu. "Positive solution to a singular $(k,n-k)$ conjugate boundary value problem." Mathematica Bohemica 136, no. 1 (2011): 69–79. http://dx.doi.org/10.21136/mb.2011.141451.

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17

Qiu, Yu-Yang. "Numerical method to a class of boundary value problems." Thermal Science 22, no. 4 (2018): 1877–83. http://dx.doi.org/10.2298/tsci1804877q.

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A class of boundary value problems can be transformed uniformly to a least square problem with Toeplitz constraint. Conjugate gradient least square, a matrix iteration method, is adopted to solve this problem, and the solution process is elucidated step by step so that the example can be used as a paradigm for other applications.

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18

Gustafson, Grant B. "Uniqueness intervals and two–point boundary value problems." Tatra Mountains Mathematical Publications 43, no. 1 (2009): 91–97. http://dx.doi.org/10.2478/v10127-009-0028-3.

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Abstract Consider a linear nth order differential equation with continuous coefficients and continuous forcing term. The maximal uniqueness interval for a classical 2-point boundary value problem will be calculated by an algorithm that uses an auxiliary linear system of differential equations, called a Mikusinski system. This system always has higher order than n. The algorithm leads to a graphical representation of the uniqueness profile and to a new method for solving 2-point boundary value problems. The ideas are applied to construct a graphic for the conjugate function associated with the

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19

Lyons, Jeffrey W., Jeffrey T. Neugebauer, and Aaron G. Wingo. "Existence and Nonexistence of Positive Solutions for Fractional Boundary Value Problems with Lidstone-Inspired Fractional Conditions." Mathematics 13, no. 8 (2025): 1336. https://doi.org/10.3390/math13081336.

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This paper investigates the existence and nonexistence of positive solutions for a class of nonlinear Riemann–Liouville fractional boundary value problems of order α+2n, where α∈(m−1,m] with m≥3 and m,n∈N. The conjugate fractional boundary conditions are inspired by Lidstone conditions. The nonlinearity depends on a positive parameter on which we identify constraints that determine the existence or nonexistence of positive solutions. Our method involves constructing Green’s function by convolving the Green functions of a lower-order fractional boundary value problem and a conjugate boundary va

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20

Lan, K. Q. "Multiple positive solutions of conjugate boundary value problems with singularities." Applied Mathematics and Computation 147, no. 2 (2004): 461–74. http://dx.doi.org/10.1016/s0096-3003(02)00739-7.

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21

Jiang, Weihua, and Jinlian Zhang. "Positive solutions for conjugate boundary value problems in Banach spaces." Nonlinear Analysis: Theory, Methods & Applications 71, no. 3-4 (2009): 723–29. http://dx.doi.org/10.1016/j.na.2008.10.104.

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22

Eloe, Paul W., Darrel Hankerson, and Johnny Henderson. "Positive solutions and conjugate points for multipoint boundary value problems." Journal of Differential Equations 95, no. 1 (1992): 20–32. http://dx.doi.org/10.1016/0022-0396(92)90041-k.

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23

Lou, Bendong. "Solutions for superlinear ( n − 1, 1) conjugate boundary value problems." Acta Mathematica Scientia 21, no. 2 (2001): 259–64. http://dx.doi.org/10.1016/s0252-9602(17)30408-3.

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24

Nicolaides, R. A. "Deflation of Conjugate Gradients with Applications to Boundary Value Problems." SIAM Journal on Numerical Analysis 24, no. 2 (1987): 355–65. http://dx.doi.org/10.1137/0724027.

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25

Tikhomirov, V. V. "Optimal control of some non-self-conjugate boundary-value problems." Computational Mathematics and Modeling 9, no. 1 (1998): 94–101. http://dx.doi.org/10.1007/bf02404089.

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26

Eloe, Paul W., and Johnny Henderson. "Positive solutions for (n − 1, 1) conjugate boundary value problems." Nonlinear Analysis: Theory, Methods & Applications 28, no. 10 (1997): 1669–80. http://dx.doi.org/10.1016/0362-546x(95)00238-q.

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27

Agarwal, Ravi P., and Donal O'Regan. "Positive Solutions for (p,n−p) Conjugate Boundary Value Problems." Journal of Differential Equations 150, no. 2 (1998): 462–73. http://dx.doi.org/10.1006/jdeq.1998.3501.

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28

Sun, Qiao, and Yujun Cui. "Solvability of (k,n-k) Conjugate Boundary Value Problems with Integral Boundary Conditions at Resonance." Journal of Function Spaces 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/3454879.

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We investigate a (k,n-k) conjugate boundary value problem with integral boundary conditions. By using Mawhin continuation theorem, we study the solvability of this boundary value problem at resonance. It is shown that the boundary value problem (-1)n-kφ(n)(x)=fx,φx,φ′x,…,φ(n-1)(x), x∈[0,1], φ(i)(0)=φ(j)(1)=0, 1≤i≤k-1, 0≤j≤n-k-1, φ(0)=∫01φ(x)dA(x) has at least one solution under some suitable conditions.

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29

Chyan, Chuan Jen, and Patricia J. Y. Wong. "MULTIPLE POSITIVE SOLUTIONS OF CONJUGATE BOUNDARY VALUE PROBLEMS ON TIME SCALES." Taiwanese Journal of Mathematics 11, no. 2 (2007): 421–45. http://dx.doi.org/10.11650/twjm/1500404700.

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30

Cui, Yujun, and Yumei Zou. "Monotone iterative technique for $(k, n-k)$ conjugate boundary value problems." Electronic Journal of Qualitative Theory of Differential Equations, no. 69 (2015): 1–11. http://dx.doi.org/10.14232/ejqtde.2015.1.69.

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31

Zu, Li, Daqing Jiang, Yongjie Gai, Donal O’Regan, and Haiyin Gao. "Weak singularities and existence of solutions to conjugate boundary value problems." Nonlinear Analysis: Real World Applications 10, no. 5 (2009): 2627–32. http://dx.doi.org/10.1016/j.nonrwa.2008.05.013.

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32

Zheng, Bo. "Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems." Discrete Dynamics in Nature and Society 2010 (2010): 1–26. http://dx.doi.org/10.1155/2010/364079.

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We consider the existence and multiplicity of solutions to discrete conjugate boundary value problems. A generalized asymptotically linear condition on the nonlinearity is proposed, which includes the asymptotically linear as a special case. By classifying the linear systems, we define index functions and obtain some properties and the concrete computation formulae of index functions. Then, some new conditions on the existence and multiplicity of solutions are obtained by combining some nonlinear analysis methods, such as Leray-Schauder principle and Morse theory. Our results are new even for

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33

Ma, Ruyun. "Positive Solutions for Semipositone (k,n−k) Conjugate Boundary Value Problems." Journal of Mathematical Analysis and Applications 252, no. 1 (2000): 220–29. http://dx.doi.org/10.1006/jmaa.2000.6987.

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34

JIANG, Daqing, and Huizhao LIU. "EXISTENCE OF POSITIVE SOLUTIONS TO (k, n-k) CONJUGATE BOUNDARY VALUE PROBLEMS †." Kyushu Journal of Mathematics 53, no. 1 (1999): 115–25. http://dx.doi.org/10.2206/kyushujm.53.115.

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35

Cui, Yanyan, Chaojun Wang, Yonghong Xie та Yuying Qiao. "Boundary value problems of conjugate and generalized k-holomorphic functions in ℂ2". Acta Mathematica Scientia 44, № 5 (2024): 1837–52. http://dx.doi.org/10.1007/s10473-024-0511-6.

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36

Henderson, Johnny, and William Yin. "Singular (k, n − k) boundary value problems between conjugate and right focal." Journal of Computational and Applied Mathematics 88, no. 1 (1998): 57–69. http://dx.doi.org/10.1016/s0377-0427(97)00207-0.

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37

Кержаев, А. П., И. В. Меньшова, and А. В. Никитин. "On solving boundary value problems for an elastic half-strip with mixed boundary conditions at the end." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 3(57) (December 29, 2023): 51–58. http://dx.doi.org/10.37972/chgpu.2023.57.3.003.

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В статье рассмотрена краевая задача теории упругости для полуполосы со смешанными граничными условиями на ее торце. Граничные условия на длинных сторонах соответствуют периодическому продолжению решения в полуплоскость, т.е. решение представляется в виде тригонометрических рядов Фурье. Построено точное решение задачи, основанное на использовании сопряженных тригонометрических рядов. The paper deals with a boundary value problem of the theory of elasticity for a half-strip with mixed boundary conditions at its end. The boundary conditions on the long sides correspond to the periodic continuatio

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38

Tkachev, Alexander, Dmitry Chernoivan, and Alexander Pashkovskiy. "Solving boundary value problems in modeling physical fields in bounded and unbounded multilinked domains using combined mesh-free methods." Известия высших учебных заведений. Электромеханика 67, no. 3 (2024): 6–16. http://dx.doi.org/10.17213/0136-3360-2024-3-6-16.

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The article considers the problem of modeling stationary physical fields at a given source distribution on the plane. Boundary value problems with boundary conditions of the first and second kind are formulated, the solution of which is sought using conjugate field potentials by the combined mesh-free methods of fundamental solutions and Monte Carlo. The fundamental solutions of the Laplace equation and their conjugate functions are used as basic functions for the approximate solution of boundary value problems. The peculiarities of applying the method of fundamental solu-tions in relation to

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39

Мартыненко, С. И. "On the approximation error in the problems of conjugate convective heat transfer." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 4 (September 10, 2019): 438–43. http://dx.doi.org/10.26089/nummet.v20r438.

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Рассмотрено влияние малых возмущений границы области на погрешность аппроксимации модельной краевой задачи. Показано, что игнорирование малых возмущений границы приводит к дополнительной погрешности аппроксимации исходной дифференциальной задачи, не связанной с шагом сетки. Полученные результаты представляют интерес для математического моделирования сопряженного теплообмена, моделирования течений с поверхностными химическими реакциями и других приложений, связанных с течениями рабочих сред вблизи шероховатых поверхностей. The effects of small boundary perturbation on the approximation error fo

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40

Eloe, P. W., and P. L. Saintignon. "Method of Forced Monotonicity for Conjugate type Boundary Value Problems for Ordinary Differential Equations." Canadian Mathematical Bulletin 31, no. 1 (1988): 79–84. http://dx.doi.org/10.4153/cmb-1988-012-0.

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AbstractLet I = [a, b] ⊆ R and let L be an nth order linear differential operator defined on Cn(I). Let 2 ≦ k ≦ n and let a ≦ x1 < x2 < … < xn = b. A method of forced mono tonicity is used to construct monotone sequences that converge to solutions of the conjugate type boundary value problem (BVP) Ly = f(x, y),y(i-1) = rij where 1 ≦i ≦ mj, 1 ≦ j ≦ k, mj = n, and f : I X R → R is continuous. A comparison theorem is employed and the method requires that the Green's function of an associated BVP satisfies certain sign conditions.

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41

Zhao, Yulin. "Positive Solutions for (k,n−k) Conjugate Multipoint Boundary Value Problems in Banach Spaces." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/727468.

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By means of the fixed point index theory of strict-set contraction operator, we study the existence of positive solutions for the multipoint singular boundary value problem(-1)n-kun(t)=f(t,ut),0<t<1,n≥2,1≤k≤n-1,u(0)=∑i=1m-2‍aiu(ξi),u(i)(0)=u(j)(1)=θ,1≤i≤k−1,0≤j≤n−k−1in a real Banach spaceE, whereθis the zero element ofE,0<ξ1<ξ2<⋯<ξm-2<1,ai∈[0,+∞),i=1,2,…,m-2.As an application, we give two examples to demonstrate our results.

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42

Lin, Xiaoning, Daqing Jiang, and Xiaoyue Li. "Existence and uniqueness of solutions for singular (k, n - k) conjugate boundary value problems." Computers & Mathematics with Applications 52, no. 3-4 (2006): 375–82. http://dx.doi.org/10.1016/j.camwa.2006.03.019.

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43

Glowinski, R., H. B. Keller, and L. Reinhart. "Continuation-Conjugate Gradient Methods for the Least Squares Solution of Nonlinear Boundary Value Problems." SIAM Journal on Scientific and Statistical Computing 6, no. 4 (1985): 793–832. http://dx.doi.org/10.1137/0906055.

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44

Kong, Lingbin, and Junyu Wang. "The Green's Function for (k,n−k) Conjugate Boundary Value Problems and Its Applications." Journal of Mathematical Analysis and Applications 255, no. 2 (2001): 404–22. http://dx.doi.org/10.1006/jmaa.2000.7158.

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45

Wang, Yongqing. "Existence of Uniqueness and Nonexistence Results of Positive Solution for Fractional Differential Equations Integral Boundary Value Problems." Journal of Function Spaces 2018 (December 4, 2018): 1–7. http://dx.doi.org/10.1155/2018/1547293.

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In this paper, we consider a class of fractional differential equations with conjugate type integral conditions. Both the existence of uniqueness and nonexistence of positive solution are obtained by means of the iterative technique. The interesting point lies in that the assumption on nonlinearity is closely associated with the spectral radius corresponding to the relevant linear operator.

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46

Imanbetova, A. B., A. A. Sarsenbi, and B. Seilbekov. "On solvability of the inverse problem for a fourth-order parabolic equation with a complex-valued coefficient." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 113, no. 1 (2024): 60–72. http://dx.doi.org/10.31489/2024m1/60-72.

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In this paper, the inverse problem for a fourth-order parabolic equation with a variable complex-valued coefficient is studied by the method of separation of variables. The properties of the eigenvalues of the Dirichlet and Neumann boundary value problems for a non-self-conjugate fourth-order ordinary differential equation with a complex-valued coefficient are established. Known results on the Riesz basis property of eigenfunctions of boundary value problems for ordinary differential equations with strongly regular boundary conditions in the space L2(−1,1) are used. On the basis of the Riesz b

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47

FAN, Jinjun, and Yinghua YANG. "Singular (n-1,n) Conjugate Boundary Value Problems in Banach Spaces." Acta Analysis Functionalis Applicata 12, no. 1 (2010): 79–82. http://dx.doi.org/10.3724/sp.j.1160.2010.00079.

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48

Glowinski, Roland, and Qiaolin He. "A Least-Squares/Fictitious Domain Method for Linear Elliptic Problems with Robin Boundary Conditions." Communications in Computational Physics 9, no. 3 (2011): 587–606. http://dx.doi.org/10.4208/cicp.071009.160310s.

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AbstractIn this article, we discuss a least-squares/fictitious domain method for the solution of linear elliptic boundary value problems with Robin boundary conditions. Let Ω and ω be two bounded domains of Rd such that ω̅⊂Ω. For a linear elliptic problem in Ω\ω̅ with Robin boundary condition on the boundary ϒ of ω, our goal here is to develop a fictitious domain method where one solves a variant of the original problem on the full Ω, followed by a well-chosen correction over ω. This method is of the virtual control type and relies on a least-squares formulation making the problem solvable by

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49

GRAVVANIS, GEORGE A., and KONSTANTINOS M. GIANNOUTAKIS. "ON THE RATE OF CONVERGENCE AND COMPLEXITY OF NORMALIZED IMPLICIT PRECONDITIONING FOR SOLVING FINITE DIFFERENCE EQUATIONS IN THREE SPACE VARIABLES." International Journal of Computational Methods 01, no. 02 (2004): 367–86. http://dx.doi.org/10.1142/s0219876204000174.

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Normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite difference method of partial differential equations in three space variables, are presented. Normalized implicit preconditioned conjugate gradient-type schemes in conjunction with normalized approximate factorization procedures are presented for the efficient solution of sparse linear systems. The convergence analysis with theoretical estimates on the rate of convergence and computational complexity of the normalized implicit preconditioned conjugate gradient method are also giv

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50

Tkachev, Alexander, Dmitry Chernoivan, and Nikolay Savelov. "A Combined Mesh-Free Method for Solving the Mixed Boundary Value Problems in Modeling the Potential Physical Fields." Известия высших учебных заведений. Электромеханика 65, no. 4 (2022): 3–14. http://dx.doi.org/10.17213/0136-3360-2022-4-3-14.

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The article describes a combined mesh-free method for solving mixed boundary value problems for the Laplace equa-tion arising from the analysis of potential physical fields in homogeneous media. The solution using mesh-free meth-ods of fundamental solutions and the Monte Carlo method is found. The modification of these methods is carried out taking into account the features that arise when setting mixed boundary conditions at the computational domain boundary. The conjugate fundamental solutions of the Laplace equation and the procedure of random walk by spheres are used, taking into account t

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