Nonlinear Urysohn discrete equations on the infinite interval: a fixed-point approach
type: Item
instance of: scholarly article
title: Nonlinear Urysohn discrete equations on the infinite interval: a fixed-point approach
zbMATH Open document ID: 1003.39017
DOI: 10.1016/S0898-1221(01)00152-3
author: Ravi P. Agarwal
author: Donal O'Regan
publication date: 2002-06-13T00:00:00Z
review text: The present paper is devoted to the study of the nonlinear-Urysohn discrete equation of the form \[ y(i)= \sum^\infty_{j=0} f\bigl(i,j, y(j) \bigr), \quad i\in\{0,1,2,\dots,\} =N^+, \tag{1} \] where \(y:\mathbb{N}^+ \to \mathbb{R}\). A variety of sufficient conditions for the existence of \(C(\mathbb{N}^+, \mathbb{R})\) solutions to (1) are established by means of some new fixed-point theorems obtained by the same authors in earlier papers. Herein \(C(\mathbb{N}^+, \mathbb{R})\) denotes the class of maps \(w\) continuous on \(\mathbb{N}^+\) (discrete topology), the topology being that of uniform convergence on \(N_m=\{0,1, \dots, m\}\) for every \(m\in \mathbb{N}_0\). The results obtained extend and complement many known results in the literature which can be found in the book by \textit{R. P. Agarwal} [``Difference equations and inequalities'' Marcel Dekker New York (1992; Zbl 0925.39001)] and in the paper by the same authors [Math. Methods Appl. Sci. 22, No. 1, 91-99 (1999 Zbl 0927.47042)].
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 47H30
zbMATH DE Number: 1755249
zbMATH Keywords: discrete Urysohn equation
zbMATH Keywords: nonlinear-Urysohn discrete equation
zbMATH Keywords: fixed-point theorems
MaRDI profile type: Publication
cites work: Q4003305
cites work: Q4238717
cites work: A fixed-point approach for nonlinear discrete boundary value problems
cites work: Bounds for positive solutions for a focal boundary value problem
cites work: A discrete boundary value problem
Wikidata QID: Q126975582
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1755249