Inverse problems for first-order differential systems with periodic 2 × 2 matrix potentials and quasi-periodic boundary conditions

In the present paper, we are interested in studying first-order Stieltjes differential inclusions with periodic boundary conditions. Relying on recent results obtained by the authors in the single-valued case, the existence of regulated solutions is obtained via the multivalued Bohnenblust–Karlin fixed-point theorem and a result concerning the dependence on the data of the solution set is provided.

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First order functional differential equations with periodic boundary conditions

Applicable Analysis ◽

10.1080/00036810601124076 ◽

2007 ◽

Vol 86 (2) ◽

pp. 205-221

Author(s):

B. C. Dhage ◽

John R. Graef

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Periodic Boundary ◽

Functional Differential Equations ◽

Periodic Boundary Conditions ◽

First Order ◽

Functional Differential

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On first order differential inclusions with periodic boundary conditions

Mathematical Inequalities & Applications ◽

10.7153/mia-08-07 ◽

2005 ◽

pp. 71-78

Author(s):

Mouffak Benchohra ◽

Sotiris K. Ntouyas

Keyword(s):

Boundary Conditions ◽

Differential Inclusions ◽

Periodic Boundary ◽

Periodic Boundary Conditions ◽

First Order

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A Numerical Iterative Method for Solving Systems of First-Order Periodic Boundary Value Problems

Journal of Applied Mathematics ◽

10.1155/2014/135465 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 15

Author(s):

Mohammed AL-Smadi ◽

Omar Abu Arqub ◽

Ahmad El-Ajou

Keyword(s):

Differential Equations ◽

Iterative Method ◽

Boundary Conditions ◽

Ordinary Differential Equations ◽

Present Method ◽

Periodic Boundary ◽

Reproducing Kernel ◽

Reproducing Kernel Hilbert Space ◽

Periodic Boundary Conditions ◽

First Order

The objective of this paper is to present a numerical iterative method for solving systems of first-order ordinary differential equations subject to periodic boundary conditions. This iterative technique is based on the use of the reproducing kernel Hilbert space method in which every function satisfies the periodic boundary conditions. The present method is accurate, needs less effort to achieve the results, and is especially developed for nonlinear case. Furthermore, the present method enables us to approximate the solutions and their derivatives at every point of the range of integration. Indeed, three numerical examples are provided to illustrate the effectiveness of the present method. Results obtained show that the numerical scheme is very effective and convenient for solving systems of first-order ordinary differential equations with periodic boundary conditions.

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First Order Coupled Systems With Functional and Periodic Boundary Conditions: Existence Results and Application to an SIRS Model

Axioms ◽

10.3390/axioms8010023 ◽

2019 ◽

Vol 8 (1) ◽

pp. 23

Author(s):

João Fialho ◽

Feliz Minhós

Keyword(s):

Boundary Conditions ◽

Periodic Boundary ◽

Coupled System ◽

Periodic Boundary Conditions ◽

Existence Results ◽

Coupled Systems ◽

First Order ◽

Sirs Model ◽

Functional Boundary ◽

Functional Boundary Conditions

The results presented in this paper deal with the existence of solutions of a first order fully coupled system of three equations, and they are split in two parts: 1. Case with coupled functional boundary conditions, and 2. Case with periodic boundary conditions. Functional boundary conditions, which are becoming increasingly popular in the literature, as they generalize most of the classical cases and in addition can be used to tackle global conditions, such as maximum or minimum conditions. The arguments used are based on the Arzèla Ascoli theorem and Schauder’s fixed point theorem. The existence results are directly applied to an epidemic SIRS (Susceptible-Infectious-Recovered-Susceptible) model, with global boundary conditions.

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