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Journal articles on the topic 'Linear Ordinary Differential Equations in Banach Spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Mursaleen, M., and Syed Rizvi. "Existence results for second order linear differential equations in Banach spaces." Applicable Analysis and Discrete Mathematics 12, no. 2 (2018): 481–92. http://dx.doi.org/10.2298/aadm160902015m.

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In this paper we are concerned with the existence of solutions for certain classes of second order differential equations. First we deal with an infinite system of second order linear differential equations, which is reduced to an ordinary differential equation posed in the space of convergent sequences. Next we investigate the problem of existence for a second order differential equation posed on an arbitrary Banach space. The used approach is based on the measures of noncompactness concept, the use of Darbo's fixed point theorem and Kamke comparison functions.

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2

Providas, Efthimios, Stefanos Zaoutsos, and Ioannis Faraslis. "Closed-Form Solutions of Linear Ordinary Differential Equations with General Boundary Conditions." Axioms 10, no. 3 (September 14, 2021): 226. http://dx.doi.org/10.3390/axioms10030226.

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This paper deals with the solution of boundary value problems for ordinary differential equations with general boundary conditions. We obtain closed-form solutions in a symbolic form of problems with the general n-th order differential operator, as well as the composition of linear operators. The method is based on the theory of the extensions of linear operators in Banach spaces.

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3

Basit, Bolis, and Chuanyi Zhang. "New Almost Periodic Type Functions and Solutions of Differential Equations." Canadian Journal of Mathematics 48, no. 6 (December 1, 1996): 1138–53. http://dx.doi.org/10.4153/cjm-1996-059-9.

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AbstractLet X be a Banach space and . Let Π and Π0 be two subspaces of , the Banach space of bounded continuous functions from 𝕁 to X. We seek conditions under which Π + Π0 is closed in . This led to introduce a general space, which contains many classes of almost periodic type functions as subspaces. We prove some recent results on indefinite integral for the elements of these classes. We apply certain results on harmonic analysis to investigate solutions of differential equations. As an application we study specific spaces: the spaces of asymptotic and pseudo almost automorphic functions and their solutions of some ordinary quasi-linear and a non-linear parabolic partial differential equations.

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4

Kudryavtsev, L. D. "Stabilization of Functions and its Application." gmj 1, no. 2 (April 1994): 183–95. http://dx.doi.org/10.1515/gmj.1994.183.

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Abstract The concepts of polynomial stabilization, strong polynomial stabilization, and strong stabilization are introduced for a fundamental system of solutions of linear differential equations. Some criteria of such kinds of stabilizations and applications to the theory of existence and uniqueness of solutions of ordinary differential equations are given. An abstract scheme of the obtained results is presented for Banach spaces.

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5

Potter, A. J. B. "Approximation methods and the generalised Fuller index for semi-flows in Banach spaces." Proceedings of the Edinburgh Mathematical Society 29, no. 3 (October 1986): 299–308. http://dx.doi.org/10.1017/s0013091500017740.

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In [3] Fuller introduced an index (now called the Fuller index) in order to study periodic solutions of ordinary differential equations. The objective of this paper is to give a simple generalisation of the Fuller index which can be used to study periodic points of flows in Banach spaces. We do not claim any significant breakthrough but merely suggest that the simplistic approach, presented here, might prove useful for the study of non-linear differential equations. We show our results can be used to study functional differential equations.

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6

Bai, Meng, and Shihe Xu. "Global existence of solutions for a nonlinear size-structured population model with distributed delay in the recruitment." International Journal of Mathematics 26, no. 10 (September 2015): 1550085. http://dx.doi.org/10.1142/s0129167x15500858.

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In this paper, we study a nonlinear size-structured population model with distributed delay in the recruitment. The delayed problem is reduced into an abstract initial value problem of an ordinary differential equation in a Banach space by using the semigroup techniques. The local existence and uniqueness of solution as well as the continuous dependence on initial conditions are obtained by using the general theory of quasi-linear evolution equations in Banach spaces, while the global existence of solution is obtained by the estimates of the solution and the extension theorem.

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7

Grobbelaar-Van Dalsen, Maríe, and Niko Sauer. "Dynamic boundary conditions for the Navier–Stokes equations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 113, no. 1-2 (1989): 1–11. http://dx.doi.org/10.1017/s030821050002391x.

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SynopsisWhen a symmetric rigid body performs a rotation in a fluid, the system of governing equations consists of conservation of linear momentum of the fluid and conservation of angular momentum of the rigid body. Since the torque at the interface involves the drag due to the fluid flow, the conservation of angular momentum may be viewed as a boundary condition for the field equations of fluid motion. These equations at the boundary contain a time derivative and thus are of a dynamic nature. The familiar no-slip condition becomes an additional equation in the system which not only governs the fluid motion, but also the motion of the rigid body. The unknown functions in the system of equations are the velocity and pressure fields of the fluid motion and the angular velocity of the rigid body.In this paper we formulate the physical problem for the case of rotation about an axis of symmetry as an abstract ordinary differential equation in two Banach spaces in which the velocity field is the only unknown. To achieve this, a method for the elimination of the pressure field, which also occurs in the boundary condition, is developed. Existence and uniqueness results for the abstract equation are derived with the aid of the theory of B-evolutions and the associated theory of fractional powers of a closed pair of operators.

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8

Hájek, Petr, and Paola Vivi. "Some problems on ordinary differential equations in Banach spaces." Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 104, no. 2 (September 2010): 245–55. http://dx.doi.org/10.5052/racsam.2010.16.

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9

O'Regan, D. "Weak solutions of ordinary differential equations in Banach spaces." Applied Mathematics Letters 12, no. 1 (January 1999): 101–5. http://dx.doi.org/10.1016/s0893-9659(98)00133-5.

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10

Redheffer, Ray, and Wolfgang Walter. "Remarks on ordinary differential equations in ordered Banach spaces." Monatshefte f�r Mathematik 102, no. 3 (September 1986): 237–49. http://dx.doi.org/10.1007/bf01294602.

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11

Hassan, Ezzat R., M. Sh Alhuthali, and M. M. Al-Ghanmi. "Generalized Uniqueness Theorem for Ordinary Differential Equations in Banach Spaces." Scientific World Journal 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/272479.

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We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well.

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12

Appell, J., and P. P. Zabrejko. "LINEAR DIFFERENTIAL EQUATIONS IN SCALES OF BANACH SPACES." Analysis 12, no. 1-2 (June 1992): 31–46. http://dx.doi.org/10.1524/anly.1992.12.12.31.

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13

Banaś, Józef. "On existence theorems for differential equations in Banach spaces." Bulletin of the Australian Mathematical Society 32, no. 1 (August 1985): 73–82. http://dx.doi.org/10.1017/s0004972700009734.

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14

Lyubich, Yu, and Phóng Vũ. "Asymptotic stability of linear differential equations in Banach spaces." Studia Mathematica 88, no. 1 (1988): 37–42. http://dx.doi.org/10.4064/sm-88-1-37-42.

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15

WU, JING. "WIENER–POISSON TYPE MULTIVALUED STOCHASTIC EVOLUTION EQUATIONS IN BANACH SPACES." Stochastics and Dynamics 12, no. 02 (April 8, 2012): 1150015. http://dx.doi.org/10.1142/s0219493712003687.

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We prove the existence and uniqueness of solutions to Wiener–Poisson type multivalued stochastic evolution equations in abstract spaces. We also prove that the solution has the Markov property. Moreover, applications to stochastic ordinary differential equations and stochastic partial differential equations are presented.

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16

Hájek, Petr, and Paola Vivi. "On ω-limit sets of ordinary differential equations in Banach spaces." Journal of Mathematical Analysis and Applications 371, no. 2 (November 2010): 793–812. http://dx.doi.org/10.1016/j.jmaa.2010.05.059.

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17

Appell, Jürgen, Martin Väth, and A. Vignoli. "Compactness and Existence Results for Ordinary Differential Equations in Banach Spaces." Zeitschrift für Analysis und ihre Anwendungen 18, no. 3 (1999): 569–84. http://dx.doi.org/10.4171/zaa/899.

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18

Song, Zai-Feng. "Existence of generalized solutions for ordinary differential equations in Banach spaces." Journal of Mathematical Analysis and Applications 128, no. 2 (December 1987): 405–12. http://dx.doi.org/10.1016/0022-247x(87)90192-2.

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19

Ashurov, R. R., and W. N. Everitt. "Linear quasi-differential operators in locally integrable spaces on the real line." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 4 (August 2000): 671–98. http://dx.doi.org/10.1017/s0308210500000366.

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The theory of ordinary linear quasi-differential expressions and operators has been extensively developed in integrable-square Hilbert spaces. There is also an extensive theory of ordinary linear differential expressions and operators in integrable-p Banach spaces.However, the basic definition of linear quasi-differential expressions involves Lebesgue locally integrable spaces on intervals of the real line. Such spaces are not Banach spaces but can be considered as complete locally convex linear topological spaces where the topology is derived from a countable family of semi-norms. The first conjugate space can also be defined as a complete locally convex linear topological space, but now with the topology derived as a strict inductive limit.This paper develops the properties of linear quasi-differential operators in a locally integrable space and the first conjugate space. Conjugate and preconjugate operators are defined in, respectively, dense and total domains.

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20

Liang, Jin, and Tijun Xiao. "Functional differential equations with infinite delay in Banach spaces." International Journal of Mathematics and Mathematical Sciences 14, no. 3 (1991): 497–508. http://dx.doi.org/10.1155/s0161171291000686.

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In this paper, a definition of the fundamental operator for the linear autonomous functional differential equation with infinite delay in a Banach space is given, and some sufficient and necessary conditions of the fundamental operator being exponentially stable in abstract phase spaces which satisfy some suitable hypotheses are obtained. Moreover, we discuss the relation between the exponential asymptotic stability of the zero solution of nonlinear functional differential equation with infinite delay in a Banach space and the exponential stability of the solution semigroup of the corresponding linear equation, and find that the exponential stability problem of the zero solution for the nonlinear equation can be discussed only in the exponentially fading memory phase space.

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21

Xiao, Ti-Jun, and Liang Jin. "On complete second order linear differential equations in Banach spaces." Pacific Journal of Mathematics 142, no. 1 (March 1, 1990): 175–95. http://dx.doi.org/10.2140/pjm.1990.142.175.

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22

Chinnì, Antonia, and Paolo Cubiotti. "Partial differential equations in Banach spaces involving nilpotent linear operators." Annales Polonici Mathematici 65, no. 1 (1996): 67–80. http://dx.doi.org/10.4064/ap-65-1-67-80.

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23

Horia Popescu, Liviu. "A topological classification of linear differential equations on Banach spaces." Journal of Differential Equations 203, no. 1 (August 2004): 28–37. http://dx.doi.org/10.1016/j.jde.2004.03.038.

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24

Derevenskii, V. P. "Linear ordinary differential equations with constant coefficients over a Banach algebra." Mathematical Notes 84, no. 3-4 (October 2008): 342–55. http://dx.doi.org/10.1134/s0001434608090046.

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25

Barnes, Benedict, I. A. Adjei, S. K. Amponsah, and E. Harris. "Product-Normed Linear Spaces." European Journal of Pure and Applied Mathematics 11, no. 3 (July 31, 2018): 740–50. http://dx.doi.org/10.29020/nybg.ejpam.v11i3.3284.

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In this paper, both the product-normed linear space $P-NLS$ (product-Banach space) and product-semi-normed linear space (product-semi-Banch space) are introduced. These normed linear spaces are endowed with the first and second product inequalities, which have a lot of applications in linear algebra and differential equations. In addition, we showed that $P-NLS$ admits functional properties such as completeness, continuity and the fixed point.

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26

Neuman, František. "Limit Behavior of Solutions of Ordinary Linear Differential Equations." gmj 1, no. 3 (June 1994): 315–23. http://dx.doi.org/10.1515/gmj.1994.315.

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Abstract A classification of classes of equivalent linear differential equations with respect to ω-limit sets of their canonical representatives is introduced. Some consequences of this classification to the oscillatory behavior of solution spaces are presented.

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27

Çavuş, Abdullah, Djavvat Khadjiev, and Seda Öztürk. "On periodic solutions to nonlinear differential equations in Banach spaces." Filomat 30, no. 4 (2016): 1069–76. http://dx.doi.org/10.2298/fil1604069c.

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Let A denote the generator of a strongly continuous periodic one-parameter group of bounded linear operators in a complex Banach space H. In this work, an analog of the resolvent operator which is called quasi-resolvent operator and denoted by R? is defined for points of the spectrum, some equivalent conditions for compactness of the quasi-resolvent operators R? are given. Then using these, some theorems on existence of periodic solutions to the non-linear equations ?(A)x = f (x) are given, where ?(A) is a polynomial of A with complex coefficients and f is a continuous mapping of H into itself.

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28

Prilepko, A. I. "Optimal control and maximum principle in (B)-spaces. Examples for partial differential equations in (H)-spaces and ordinary differential equations in Rn." Доклады Академии наук 489, no. 1 (November 10, 2019): 11–16. http://dx.doi.org/10.31857/s0869-5652489111-16.

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Observation and control problems in Banach (B)-spaces are investigated. On the basis of the BUME method and the monotone mapping method, a criterion of controllability and optimal controllability is formulated. The inverse controllability problem is introduced and an abstract maximum principle is formulated in (B)-spaces. For PDE in Hilbert (H)-spaces and for ODE in Rn, the integral maximum principle is proved and the optimality system is written out.

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29

Sklyar, G. M. "On the Maximal Asymptotics for Linear Differential Equations in Banach Spaces." Taiwanese Journal of Mathematics 14, no. 6 (December 2010): 2203–17. http://dx.doi.org/10.11650/twjm/1500406070.

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30

Trenogin, V. A. "Linear approximations for differential equations in Banach spaces and Lyapunov stability." Doklady Mathematics 80, no. 2 (October 2009): 724–27. http://dx.doi.org/10.1134/s106456240905024x.

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31

Sklyar, G. M. "Lack of maximal asymptotics for linear differential equations in Banach spaces." Doklady Mathematics 81, no. 2 (April 2010): 265–67. http://dx.doi.org/10.1134/s1064562410020286.

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32

Heikkilä, S., and S. Leela. "On second order discontinuous differential equations in Banach spaces." Journal of Applied Mathematics and Stochastic Analysis 6, no. 4 (January 1, 1993): 303–23. http://dx.doi.org/10.1155/s1048953393000279.

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In this paper we study a second order semilinear initial value problem (IVP), where the linear operator in the differential equation is the infinitesimal generator of a strongly continuous cosine family in a Banach space E. We shall first prove existence, uniqueness and estimation results for weak solutions of the IVP with Carathéodory type of nonlinearity, by using a comparison method. The existence of the extremal mild solutions of the IVP is then studied when E is an ordered Banach space. We shall also discuss the dependence of these solutions on the data. A characteristic feature of the results concerning extremal solutions is that the nonlinearity is not assumed to be continuous in any of its arguments. Moreover, no compactness conditions are assumed. The obtained results are then applied to a second order partial differential equation of hyperbolic type.

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33

Su, Hua. "The Solutions of Mixed Monotone Fredholm-Type Integral Equations in Banach Spaces." Discrete Dynamics in Nature and Society 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/604105.

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By introducing new definitions ofϕconvex and-φconcave quasioperator andv0quasilower andu0quasiupper, by means of the monotone iterative techniques without any compactness conditions, we obtain the iterative unique solution of nonlinear mixed monotone Fredholm-type integral equations in Banach spaces. Our results are even new toϕconvex and-φconcave quasi operator, and then we apply these results to the two-point boundary value problem of second-order nonlinear ordinary differential equations in the ordered Banach spaces.

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34

Fitzgibbon, W. E. "Weakly continuous accretive operators in general Banach spaces." Bulletin of the Australian Mathematical Society 41, no. 2 (April 1990): 185–99. http://dx.doi.org/10.1017/s0004972700017998.

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Global wellposedness theorems are established for a class of abstract Cauchy initial value problems and a class of abstract Volterra equations which have a linear semigroup as a convolution kernel. These existence theorems are used to show that a class of nonlinear operators and a class of perturbed linear operators are m-accretive. The m-accretiveness results are used in turn to represent solutions to the differential and integral equations.

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35

Ugowski, Henryk. "On Certain Singular Ordinary Differential Equations of the First Order in Banach Spaces." Zeitschrift für Analysis und ihre Anwendungen 11, no. 1 (1992): 93–105. http://dx.doi.org/10.4171/zaa/623.

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36

Herzog, Gerd. "AN EXISTENCE AND UNIQUENESS THEOREM FOR ORDINARY DIFFERENTIAL EQUATIONS IN ORDERED BANACH SPACES." Demonstratio Mathematica 30, no. 4 (October 1, 1997): 735–40. http://dx.doi.org/10.1515/dema-1997-0404.

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37

Bu, Shangquan, and Gang Cai. "Well-posedness of fractional degenerate differential equations in Banach spaces." Fractional Calculus and Applied Analysis 22, no. 2 (April 24, 2019): 379–95. http://dx.doi.org/10.1515/fca-2019-0023.

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Abstract We study the well-posedness of the fractional degenerate differential equation: Dα (Mu)(t) + cDβ(Mu)(t) = Au(t) + f(t), (0 ≤ t ≤ 2π) on Lebesgue-Bochner spaces Lp(𝕋; X) and periodic Besov spaces $\begin{array}{} B_{p,q}^s \end{array}$ (𝕋; X), where A and M are closed linear operators in a complex Banach space X satisfying D(A) ⊂ D(M), c ∈ ℂ and 0 < β < α are fixed. Using known operator-valued Fourier multiplier theorems, we give necessary and sufficient conditions for Lp-well-posedness and $\begin{array}{} B_{p,q}^s \end{array}$-well-posedness of above equation.

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38

Diagana, Toka. "C0-semigroups of linear operators on some ultrametric Banach spaces." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–9. http://dx.doi.org/10.1155/ijmms/2006/52398.

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C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization ofC0-semigroups on (ultrametric) free Banach spacesE. In contrast with the classical setting, the parameter of a givenC0-semigroup belongs to a clopen ballΩrof the ground fieldK. As an illustration, we will discuss the solvability of some homogeneousp-adic differential equations.

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39

Chen, Guoliang, Yimin Wei, and Yifeng Xue. "The generalized condition numbers of bounded linear operators in Banach spaces." Journal of the Australian Mathematical Society 76, no. 2 (April 2004): 281–90. http://dx.doi.org/10.1017/s1446788700008958.

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AbstractFor any bounded linear operator A in a Banach space, two generalized condition numbers, k(A) and k(A) are defined in this paper. These condition numbers may be applied to the perturbation analysis for the solution of ill-posed differential equations and bounded linear operator equations in infinite dimensional Banach spaces. Different expressions for the two generalized condition numbers are discussed in this paper and applied to the perturbation analysis of the operator equation.

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40

Rapp, Piotr. "Point initial value problem for linear functional differential equations in Banach spaces." Aequationes Mathematicae 41, no. 1 (March 1991): 136–60. http://dx.doi.org/10.1007/bf02227450.

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41

Cuesta, Eduardo, and Rodrigo Ponce. "Hölder regularity for abstract semi-linear fractional differential equations in Banach spaces." Computers & Mathematics with Applications 85 (March 2021): 57–68. http://dx.doi.org/10.1016/j.camwa.2021.01.010.

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42

Mahmudov, N. I. "Approximate Controllability of Fractional Neutral Evolution Equations in Banach Spaces." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/531894.

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We discuss the approximate controllability of semilinear fractional neutral differential systems with infinite delay under the assumptions that the corresponding linear system is approximately controllable. Using Krasnoselkii's fixed-point theorem, fractional calculus, and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional neutral differential equations with infinite delay are formulated and proved. The results of the paper are generalization and continuation of the recent results on this issue.

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43

Zhao, Zengqin, and Xinsheng Du. "Positive Fixed Points for Semipositone Operators in Ordered Banach Spaces and Applications." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/406727.

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The theory of semipositone integral equations and semipositone ordinary differential equations has been emerging as an important area of investigation in recent years, but the research on semipositone operators in abstract spaces is yet rare. By employing a well-known fixed point index theorem and combining it with a translation substitution, we study the existence of positive fixed points for a semipositone operator in ordered Banach space. Lastly, we apply the results to Hammerstein integral equations of polynomial type.

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44

FAVINI, A., and A. LORENZI. "SINGULAR INTEGRO-DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE AND INVERSE PROBLEMS." Mathematical Models and Methods in Applied Sciences 13, no. 12 (December 2003): 1745–66. http://dx.doi.org/10.1142/s0218202503003100.

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We prove a global existence and uniqueness result for the recovery of unknown scalar kernels in linear singular first-order integro-differential initial-boundary value problems in Banach spaces. To this end use is made of suitable weighted Lp-spaces. Finally, we give a few applications to explicit singular partial integro-differential equations of parabolic type.

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45

Zhiqing, Han. "FIXED POINT THEOREMS OF STRICT SET-CONTRACTIONS VIA ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES." Quaestiones Mathematicae 22, no. 2 (June 1999): 171–81. http://dx.doi.org/10.1080/16073606.1999.9632071.

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46

Chen, Haibo, and Peiluan Li. "Three-point boundary value problems for second-order ordinary differential equations in Banach spaces." Computers & Mathematics with Applications 56, no. 7 (October 2008): 1852–60. http://dx.doi.org/10.1016/j.camwa.2008.04.024.

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47

Kiskinov, Hristo, and Andrey Zahariev. "Nonlinear Impulsive Differential Equations with Weighted Exponential or Ordinary Dichotomous Linear Part in a Banach Space." International Journal of Differential Equations 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/748607.

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We consider nonlinear impulsive differential equations withψ-exponential andψ-ordinary dichotomous linear part in a Banach space. By the help of Banach’s fixed-point principle sufficient conditions are found for the existence ofψ-bounded solutions of these equations onRandR+.

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48

Reinfelds, Andrejs, and Lelde Sermone. "Stability of Impulsive Differential Systems." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/253647.

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The asymptotic phase property and reduction principle for stability of a trivial solution is generalized to the case of the noninvertible impulsive differential equations in Banach spaces whose linear parts split into two parts and satisfy the condition of separation.

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49

Zabreiko, Petr P., and Svetlana V. Ponomareva. "SOLVABILITY OF THE CAUCHY PROBLEM FOR EQUATIONS WITH RIEMANN–LIOUVILLE’S FRACTIONAL DERIVATIVES." Doklady of the National Academy of Sciences of Belarus 62, no. 4 (September 13, 2018): 391–97. http://dx.doi.org/10.29235/1561-8323-2018-62-4-391-397.

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In this article we study the solvability of the analogue of the Cauchy problem for ordinary differential equations with Riemann–Liouville’s fractional derivatives with a nonlinear restriction on the right-hand side of functions in certain spaces. The conditions for solvability of the problem under consideration in given function spaces, as well as the conditions for existence of a unique solution are given. The study uses the method of reducing the problem to the second-kind Volterra equation, the Schauder principle of a fixed point in a Banach space, and the Banach-Cachoppoli principle of a fixed point in a complete metric space.

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50

Philos, Christos G., and Ioannis K. Purnaras. "A boundary value problem on the whole line to second order nonlinear differential equations." gmj 17, no. 2 (June 2010): 373–90. http://dx.doi.org/10.1515/gmj.2010.014.

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Abstract Second order nonlinear ordinary differential equations are considered, and a certain boundary value problem on the whole line is studied. Two theorems are obtained as main results. The first theorem is established by the use of the Schauder theorem and concerns the existence of solutions, while the second theorem is concerned with the existence and uniqueness of solutions and is derived by the Banach contraction principle. These two theorems are applied, in particular, to the specific class of second order nonlinear ordinary differential equations of Emden–Fowler type and to the special case of second order linear ordinary differential equations, respectively.

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