Existence and Uniqueness of Solutions for the System of First-order Nonlinear Differential Equations with Three-point and Integral Boundary Conditions

Abstract

In the paper, the existence and uniqueness of the solutions for the system of the nonlinear first-order ordinary differential equations with three-point and integral boundary conditions are studied. The Green function is constructed and the considered problem is reduced to the equivalent integral equation. The existence and uniqueness of the solutions for the given problem are analyzed by using the Banach contraction principle. The Schaefer’s fixed point theorem is thenused to prove the existence of the solutions. Finally, the examples are given to verify the given theorems.