A solution of a nonlinear integral equation
type: Item
instance of: scholarly article
title: A solution of a nonlinear integral equation
zbMATH Open document ID: 1068.45005
DOI: 10.1016/S0096-3003(03)00613-1
author: M. A. Abdou
author: E. I. Deebs
author: Wagdy Gomaa El-Sayed
published in: Applied Mathematics and Computation
publication date: 2005-02-23T00:00:00Z
review text: Among various frequently used linear and nonlinear integral equations, which play important role in functional analysis, the authors consider the integral equation \[ \varphi(x,t)= f(x,t)+ \int^1_0 k(x,y) \gamma(y,\varphi(y, t))\,dy+ \int^t_0 F(t,\tau)\,\varphi(x,\tau)\,d\tau, \] where the notations are explained in the paper. Existence of the solution of the above Hammer\-stein-Volterra type equation of the second, is proved by employing the DeBlasi measure of weak non-compactness and the Schauder fixed point theorem. The paper is supported with relevant definitions and remarks. The authors give all known theorems in Section 2 as ready references. It is believed (reviewer's conjecture) that the integral equation, considered in this paper, may be studied as a distributional integral equation and, as a fractional equation.
reviewed by: P. K. Banerji
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 2137388
zbMATH Keywords: nonlinear Hammerstein-Volterra integral equation
zbMATH Keywords: Schauder fixed point theorem
zbMATH Keywords: Carathéodory condition
zbMATH Keywords: contraction mapping
zbMATH Keywords: Cauchy sequences
zbMATH Keywords: relatively compact
zbMATH Keywords: De Blasi measure of weak non-compactness
MaRDI profile type: Publication
cites work: Fredholm-Volterra integral equation of the first kind and contact problem
cites work: Integral equation of mixed type and integrals of orthogonal polynomials
cites work: On a method for solving an integral equation in the displacement contact problem.
cites work: Q5674478
cites work: Q4748689
cites work: Q5522633
cites work: Q5544938
cites work: Q4141664
cites work: Q4744784
cites work: Q3817127
cites work: Computational Methods for Integral Equations
cites work: Q4124250
cites work: Q3681889
full work available at URL: s0096-3003(03)00613-1
OpenAlex ID: W2072218557
description: scientific article; zbMATH DE number 2137388