Singular and nonsingular boundary value problems with sign changing nonlinearities
type: Item
instance of: scholarly article
title: Singular and nonsingular boundary value problems with sign changing nonlinearities
zbMATH Open document ID: 0976.34017
DOI: 10.1155/S1025583400000345
author: Donal O'Regan
author: R. Kannan
published in: Journal of Inequalities and Applications
publication date: 2001-12-12T00:00:00Z
full work available at URL: https://eudml.org/doc/121440
review text: The authors deal with boundary value problems of the type \[ (py')'+ p(t)q(t)f(t,y)=0, \;0<t<1, \qquad \lim_{t \to 0^+} p(t)y'(t)=0; \;y(1)=A\geq 0, \] where \(1/p\) is not necessarily summable and the nonlinear term \(f\) may change sign and is not necessarily Carathéodory. Moreover, note that for \(A=0\) the problem is singular. The authors present two different approaches in order to obtain existence results. The first one is based on slight modifications on the classical upper and lower solutions technique. The second approach, valid for continuous nonlinearities \(f\), is based on certain growth conditions. Finally, the results are applied to a problem arising in the theory of shallow membrane caps.
reviewed by: Cristina Marcelli
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 74L15
zbMATH DE Number: 1563282
zbMATH Keywords: singular
zbMATH Keywords: nonlinear
zbMATH Keywords: boundary value problems
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1563282