1. bookVolume 2018 (2018): Issue 1 (December 2018)
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Format
Journal
eISSN
2544-9990
First Published
30 May 2018
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1 time per year
Languages
English
access type Open Access

Existence and uniqueness of solutions for nonlinear impulsive differential equations with three-point boundary conditions

Published Online: 26 Jul 2019
Volume & Issue: Volume 2018 (2018) - Issue 1 (December 2018)
Page range: 21 - 36
Received: 26 Dec 2018
Accepted: 22 Mar 2019
Journal Details
License
Format
Journal
eISSN
2544-9990
First Published
30 May 2018
Publication timeframe
1 time per year
Languages
English
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

MSC 2010

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