Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions
Authors: Mısır J. Mardanov,, Yagub A. Sharifov, Kamala E. Ismayilova
Journal: e-Journal of Analysis and Applied Mathematics (e-JAAM), e-ISSN 2544-9990
Volume: 2018 · Pages: 21 - 36
Published Online: 25 Jul 2019
Abstract: This paper is devoted to a system of nonlinear impulsive differential equations with three-point boundary conditions. The Green function is constructed and considered original problem is reduced to the equivalent impulsive integral equations. Sufficient conditions are found for the existence and uniqueness of solutions for the boundary value problems for the first order nonlinear system of the impulsive ordinary differential equations with three-point boundary conditions. The Banach fixed point theorem is used to prove the existence and uniqueness of a solution of the problem and Schaefer's fixed point theorem is used to prove the existence of a solution of the problem under consideration. We illustrate the application of the main results by two examples.
Keywords: Three-point boundary conditions, existence, uniqueness, fixed point, impulsive differential equations