Existence and Uniqueness of Solutions for Nonlinear Impulsive Differential Equations with Three-Point and Integral Boundary Conditions

Mardanov M. J., Sharifov Y. A., Sardarova R. A., Aliyev H. N.

AZERBAIJAN JOURNAL OF MATHEMATICS, vol.10, no.1, pp.110-126, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 1
  • Publication Date: 2020
  • Journal Name: AZERBAIJAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.110-126
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

The aim of this paper is to investigate the solution of the system of nonlinear impulsive differential equations with three-point and integral boundary conditions. The Green function is constructed and the original problem is reduced to the equivalent integral equations. Sufficient conditions are found for the existence and uniqueness of solutions to the boundary value problems for the system of first order nonlinear impulsive ordinary differential equations with three-point and integral boundary conditions. Banach's fixed point theorem is used to prove the uniqueness and Schaefer's fixed point theorem is used to prove the existence of a solution of the considered problem.