Solvability of an infinite system of nonlinear integral equations of Volterra-Hammerstein type-Reference-Cited by-同舟云学术

Solvability of an infinite system of nonlinear integral equations of Volterra-Hammerstein type

Published:2019-12-06 Issue:1 Volume:9 Page:1187-1204
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Chlebowicz Agnieszka¹

Affiliation:

1. Department of Nonlinear Analysis , Rzeszów University of Technology , Al. Powstańców Warszawy 8, 35-959 , Rzeszów , Poland

Abstract

Abstract The purpose of the paper is to study the solvability of an infinite system of integral equations of Volterra-Hammerstein type on an unbounded interval. We show that such a system of integral equations has at least one solution in the space of functions defined, continuous and bounded on the real half-axis with values in the space l 1 consisting of all real sequences whose series is absolutely convergent. To prove this result we construct a suitable measure of noncompactness in the mentioned function space and we use that measure together with a fixed point theorem of Darbo type.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

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