Positive solutions for a class of equations with a \(p\)-Laplace like operator and weights
type: Item
instance of: scholarly article
title: Positive solutions for a class of equations with a \(p\)-Laplace like operator and weights
zbMATH Open document ID: 1180.34019
author: Pavel Drábek
author: Marta Garcia-Huidobro
author: Raúl Manásevich
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-06-24T00:00:00Z
review text: The paper deals with the existence of positive solutions for the problem \[ (a(r)\varphi(u'))'+b(r)g(u)=0 \quad \text{ a.e. in}\;(0,R), \] \[ \lim_{r\to 0}a(r)\varphi(u'(r))=0, \quad u(R)=0, \] where \(\varphi\) is an odd increasing homeomorphism of \(\mathbb R\) and \(a\) and \(b\) are weight functions. To prove the main result of the paper the authors apply the Leray-Schauder degree technique. In particular, a new identity of Pohozaev type is established and used to obtain a priori bounds for positive solutions.
reviewed by: Mirosława Zima
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5569423
zbMATH Keywords: \(\varphi\)-Laplacian
zbMATH Keywords: Pohozaev identities
zbMATH Keywords: generalized Matukuma equations
zbMATH Keywords: criticality
MaRDI profile type: Publication
full work available at URL: j.na.2008.11.094
OpenAlex ID: W2014663344
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DOI: 10.1016/J.NA.2008.11.094
description: scientific article; zbMATH DE number 5569423