Existence, multiplicity and stability results for positive solutions of nonlinear \(p\)-Laplacian equations
type: Item
instance of: scholarly article
title: Existence, multiplicity and stability results for positive solutions of nonlinear \(p\)-Laplacian equations
zbMATH Open document ID: 1106.35019
DOI: 10.1142/S0252959904000287
author: Ning Su
author: Li Ma
published in: Chinese Annals of Mathematics. Series B
publication date: 2004-10-25T00:00:00Z
review text: In the present study the authors are mainly interested in the positive solutions of the following boundary value problem of nonlinear \(p\)-Laplacian equations \[ -\Delta_pu=\lambda f(u),\text{ in }\Omega\quad u=0,\text{ on }\partial\Omega,\tag{1} \] where \(\lambda>0\), \(p>1\), \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) and \(f\) is a given nonnegative, nondecreasing function. The author studies both the existence of solution to (1) and extends part of the Crandall-Rabinowitz bifurcation theory to this problem. Moreover, the stability of solutions of the parabolic counterparts of (1) is investigated.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 2109896
zbMATH Keywords: bifurcation
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Blow-up behavior for solutions of -δNu = V(x) eu in bounded domains in RN
description: scientific article; zbMATH DE number 2109896