Iterative method for solutions and coupled quasi-solutions of nonlinear Fredholm integral equations in ordered Banach spaces
type: Item
instance of: scholarly article
title: Iterative method for solutions and coupled quasi-solutions of nonlinear Fredholm integral equations in ordered Banach spaces
zbMATH Open document ID: 0862.45015
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1997-05-25T00:00:00Z
review text: The paper is concerned with new existence theorems of solutions and of coupled minimal and maximal quasi-solutions for nonlinear Fredholm integral equations by means of monotone iterative techniques. The purpose of this paper is to establish some new existence theorems on maximal and minimal solutions for integral equations in ordered Banach spaces, when the function under the integral does not possess any monotone assumption like in earlier work of \textit{D. Guo} [Northeast. Math. J. 7, No. 4, 416-423 (1991; Zbl 0755.45024)]. For preparing the main results, 5 lemmas are stated. The results obtained are applied to two-point boundary value problems of second-order nonlinear ordinary differential equations in ordered Banach spaces and to an infinite system of nonlinear integral equations of a particular form.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47H07
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 45L05
zbMATH DE Number: 955225
zbMATH Keywords: iterative method
zbMATH Keywords: minimal and maximal quasi-solutions
zbMATH Keywords: nonlinear Fredholm integral equations
zbMATH Keywords: ordered Banach spaces
zbMATH Keywords: two-point boundary value problems
zbMATH Keywords: second-order nonlinear ordinary differential equations
zbMATH Keywords: infinite system of nonlinear integral equations
author: Lishan Liu
reviewed by: Iulian Coroian
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 955225