Open AccessExistence and uniqueness of solutions for the system ofintegro-differential equations with three-point and nonlinear integral boundary conditions
Author(s) -
Mısır J. Mardanov,
Yagub A. Sharifov,
Kamala E. Ismayilova
Publication year - 2020
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2020m3/26-37
Subject(s) - mathematics , uniqueness , picard–lindelöf theorem , fixed point theorem , nonlinear system , mathematical analysis , boundary value problem , banach fixed point theorem , integral equation , uniqueness theorem for poisson's equation , differential equation , physics , quantum mechanics
The paper examines a system of nonlinear integro-differential equations with three-point and nonlinear integral boundary conditions. The original problem demonstrated to be equivalent to integral equations by using Green function. Theorems on the existence and uniqueness of a solution to the boundary value problems for the first order nonlinear system of integro- differential equations with three-point and nonlinear integral boundary conditions are proved. A proof of uniqueness theorem of the solution is obtained by Banach fixed point principle, and the existence theorem then follows from Schaefer’s theorem.