Some existence principles and some general results for singular nonlinear two point boundary value problems
type: Item
instance of: scholarly article
title: Some existence principles and some general results for singular nonlinear two point boundary value problems
zbMATH Open document ID: 0756.34030
DOI: 10.1016/0022-247X(92)90324-7
author: Donal O'Regan
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: The paper is devoted to the study of existence of solutions for singular second order nonlinear two-point boundary value problems of the form \((1/p(t))(p(t)y'(t))'+q(t)f(t,y)=0\), \(0<t<1\), where \(\lim_{y\to 0+}f(t,y)=+\infty\), uniformly on compact subsets of (0,1), and with either (i) \(y(1)=0\), \(\lim_{t\to 0+}p(t)y'(t)=0\); or (ii) \(y(0)=0\), \(y(1)=0\). Also, existence principles are presented for the general two- point boundary value problem for \((1/p(t))(p(t)y'))'+q(t)f(t,y(t)\), \(p(t)y'(t))=0\), \(0<t<1\), where \(f\) is assumed continuous. The proof uses the nonlinear alternative of Leray-Schauder. For a related work see \textit{H. Wang} [Nonlinear Anal., Theory Methods Appl. 18, No. 7, 649-655 (1992)].
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 62793
zbMATH Keywords: singular second order nonlinear two-point boundary value problems
zbMATH Keywords: nonlinear alternative of Leray-Schauder
reviewed by: Abdelkader Boucherif
MaRDI profile type: Publication
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full work available at URL: 0022-247x(92)90324-7
OpenAlex ID: W1991539185
description: scientific article; zbMATH DE number 62793