Existence of bounded solutions of integral boundary value problems for singular differential equations on whole lines
type: Item
instance of: scholarly article
title: Existence of bounded solutions of integral boundary value problems for singular differential equations on whole lines
zbMATH Open document ID: 1307.34040
DOI: 10.1142/S0129167X14500785
author: Yuji Liu
author: Shengping Chen
published in: International Journal of Mathematics
publication date: 2014-10-21T00:00:00Z
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 6359571
zbMATH Keywords: second-order differential equation
zbMATH Keywords: integral type boundary value problem
zbMATH Keywords: bounded solution
zbMATH Keywords: Leray-Schauder-type fixed point theorem
MaRDI profile type: Publication
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full work available at URL: s0129167x14500785
OpenAlex ID: W2050911649
review text: The authors prove the existence of solution to the following boundary value problem on the whole line: NEWLINE\[NEWLINE[\Phi(\rho(t)\,x'(t))]'+f(t,x(t),x'(t))=0, \quad t \in \mathbb R,NEWLINE\]NEWLINE NEWLINE\[NEWLINE\lim_{t \to - \infty}{x(t)}=\int_{-\infty}^{+ \infty}{g(s,x(s),x'(s))\, ds},NEWLINE\]NEWLINE NEWLINE\[NEWLINE\lim_{t \to + \infty}{x(t)}=\int_{-\infty}^{+ \infty}{h(s,x(s),x'(s))\, ds},NEWLINE\]NEWLINE where the involved functions satisfy suitable properties.NEWLINENEWLINEThe results follow from fixed point theory and some approximation procedure.
reviewed by: Alberto Cabada
description: scientific article; zbMATH DE number 6359571