Indefinite quasilinear elliptic equations in exterior domains with exponential critical growth.
type: Item
instance of: scholarly article
title: Indefinite quasilinear elliptic equations in exterior domains with exponential critical growth.
zbMATH Open document ID: 1249.35085
author: Luciana Roze de Freitas
author: Sérgio H. M. Soares
author: Claudianor O. Alves
published in: Differential and Integral Equations
publication date: 2012-06-07T00:00:00Z
review text: The authors study the existence of a nontrivial solution of the quasilinear elliptic problem \(-\Delta _N u + | u | ^{N-2} u = a(x) g(u)\) in \(\Omega \), \(u = 0\) on \(\partial \Omega \), where \(\Delta _{N}\) is the \(N\)-Laplacian operator, \(\Omega \subset {\mathbb R}^N\) is an exterior domain with smooth boundary, \(a(x)\) is a continuous function changing sign in \(\Omega \) and the nonlinearity \(g(u)\) has an exponential critical growth at infinity. Variational techniques are applied, in particular, the mountain pass theorem together with the Moser's function and the Trudinger-Mose inequality which enables to overcome the difficulties created by the lack of compactness in the exterior domain.
Mathematics Subject Classification ID: 35J35
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 6043413
zbMATH Keywords: quasilinear elliptic equation
zbMATH Keywords: \(N\)-Laplacian
zbMATH Keywords: exterior domain
zbMATH Keywords: exponential critical growth
zbMATH Keywords: mountain pass theorem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6043413