Existence and uniqueness results for the first-order non-linear impulsive integro-differential equations with two-point boundary conditions

Authors

  • M.J. Mardanov
  • R.S. Mammadov
  • S.Yu. Gasimov
  • Ya.A. Sharifov

DOI:

https://doi.org/10.31489/2021m2/74-83

Keywords:

two-point boundary conditions, impulsive systems, existence and uniqueness solutions, fixed point theorems, first order differential equation

Abstract

The article discusses the existence and uniqueness of solutions for a system of nonlinear integro-differential equations of the first order with two-point boundary conditions. The Green function is constructed, and the problem under consideration is reduced to equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach contraction mapping principle. Schaefer’s fixed point theorem is used to prove the existence of solutions.

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Published

30.06.2021

How to Cite

Mardanov, M.J., Mammadov, R.S., Gasimov, S.Yu., & Sharifov, Ya.A. (2021). Existence and uniqueness results for the first-order non-linear impulsive integro-differential equations with two-point boundary conditions. Bulletin of the Karaganda University. Mathematics Series, 2(102), 74–83. https://doi.org/10.31489/2021m2/74-83

Issue

No. 2 (102)/2021

Section

MATHEMATICS