On a superlinear elliptic \(p\)-Laplacian equation.
type: Item
instance of: scholarly article
title: On a superlinear elliptic \(p\)-Laplacian equation.
zbMATH Open document ID: 1087.35034
author: Zhaoli Liu
author: Thomas J. Bartsch
published in: Journal of Differential Equations
publication date: 2004-03-29T00:00:00Z
review text: The authors consider the quasilinear elliptic equation \[ -\Delta_p u= f(x,u),\quad u\in W^{1,p}_0(\Omega),\tag{1} \] on a bounded domain \(\Omega\subset \mathbb{R}^N\) with smooth boundary \(\partial\Omega\); here \(\Delta_p u=\text{div}(|\nabla u|^{p-2}\nabla u)\) is the \(p\)-Laplacian, \(p> 1\) and \(f:\overline\Omega\times \mathbb{R}\to \mathbb{R}\) is continuous. The goal of this paper is to find solutions of (1) inside or outside of certain order cones. In particular, they prove the existence of a sign changing solution when the nonlinearity \(f\) is superlinear and subcritical as \(|u|\to \infty\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 47J30
zbMATH DE Number: 2062718
zbMATH Keywords: Laplace operator
zbMATH Keywords: quasilinear Dirichlet problem
zbMATH Keywords: sign changing solution
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: j.jde.2003.08.001
OpenAlex ID: W2073693400
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DOI: 10.1016/J.JDE.2003.08.001
description: scientific article; zbMATH DE number 2062718