On the Fučík spectrum of the \(p\)-Laplacian
type: Item
instance of: scholarly article
title: On the Fučík spectrum of the \(p\)-Laplacian
zbMATH Open document ID: 1068.35086
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2004-12-16T00:00:00Z
review text: Let \(\Omega\) be a bounded domain in \({\mathbb R}^n\), \(n\geq1\). For \(1<p<\infty\), the Fucik spectrum of the \(p\)-Laplacian on \(W_0^{1,p}(\Omega)\) is defined as the set \(\Sigma_p\) of those points \((a,b)\in{\mathbb R}^2\) for which \[ -\Delta_pu=a(u^+)^{p-1}-b(u^-)^{p-1},\quad u\in W_0^{1,p}(\Omega) \] has a nontrivial solution. Here \(\Delta_pu= \operatorname{div}(| \nabla u| ^{p-2}\nabla u)\) and \(u^\pm=\max\{\pm u,0\}\). The usual spectrum of \(-\Delta_p\) corresponds to \(a=b\). The author construct and variationally characterizes by a min-max procedure an unbounded sequence of continuous and strictly decreasing curves in the Fucik spectrum of the \(p\)-Laplacian. Applications to quasilinear elliptic boundary value problems are given.
reviewed by: Andrey Ivanovic Sedov
Mathematics Subject Classification ID: 35P99
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 47J30
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 2123252
zbMATH Keywords: critical point theory on \(C^1\)-Finsler manifolds
zbMATH Keywords: quasilinear elliptic boundary value problems
zbMATH Keywords: variational methods
zbMATH Keywords: homotopical linking
author: Kanishka Perera
MaRDI profile type: Publication
full work available at URL: s00030-003-1061-6
OpenAlex ID: W2095071916
DOI: 10.1007/S00030-003-1061-6
description: scientific article; zbMATH DE number 2123252