Multiple solutions for a system of equations with \(p\)-Laplacian
type: Item
instance of: scholarly article
title: Multiple solutions for a system of equations with \(p\)-Laplacian
zbMATH Open document ID: 1155.35021
author: Shuting Cai
author: Yongqing Li
published in: Journal of Differential Equations
publication date: 2008-11-06T00:00:00Z
review text: The authors study the existence of multiple critical points of strongly indefinite nonsmooth functionals using the Limit Index, defined in \textit{Y. Q. Li} [Nonlinear Anal. TMA 25, No. 12, 1371--1389 (1995; Zbl 0847.58014)]. The results are then applied to the following boundary value problem: \[ \begin{cases} \Delta_p u=F_u(x,u,v) & \text{in }\Omega,\\ -\Delta_p v=F_v(x,u,v) & \text{in }\Omega,\\ u, v=0 & \text{on } \partial \Omega,\end{cases} \] where \(\Delta_p u=\text{div} (| \nabla u| ^{p-2}\nabla u)\), \(\Omega\) is a bounded domain in \({\mathbb R}^N\), and \(u,v\in W^{1,p}_0(\Omega)\), \(1<p<N\). Under appropriate conditions on the function \(F(x,u,v)\), the system possesses an unbounded sequence of weak solutions.
reviewed by: Yaping Liu
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 5362101
zbMATH Keywords: limit index
zbMATH Keywords: indefinite functional
zbMATH Keywords: nonsmooth
zbMATH Keywords: multiple solutions
zbMATH Keywords: \(p\)-Laplacian
MaRDI profile type: Publication
full work available at URL: j.jde.2007.12.014
OpenAlex ID: W1991692421
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DOI: 10.1016/J.JDE.2007.12.014
description: scientific article; zbMATH DE number 5362101