Nonlinear ellipticity on unbounded domains
type: Item
instance of: scholarly article
title: Nonlinear ellipticity on unbounded domains
zbMATH Open document ID: 1266.35070
DOI: 10.1216/RMJ-2012-42-6-2015
author: Victor L. Shapiro
published in: Rocky Mountain Journal of Mathematics
publication date: 2013-04-09T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmjm/1361800617
review text: Let \(\Omega\subset{\mathbb R}^N\) be an unbounded open connected set. This paper is concerned with the qualitative analysis of weak solutions of the elliptic problem \[ Lu=\lambda_1\rho u-\alpha\rho u^-+\rho g(x,u)+h\qquad\text{in}\;\Omega, \] where \(Lu=-\Delta u+q(x)u\). The main result of this paper establishes that, under some natural assumptions, this problem has a weak solution \(u\in H^1_{p,q,p}(\Omega,\Gamma)\). Examples include the Schrödinger operator, the Hermite operator, and the Laguerre operator.
reviewed by: Teodora-Liliana Rădulescu
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 6152197
zbMATH Keywords: linking theory
zbMATH Keywords: Schrödinger operators
zbMATH Keywords: singular elliptic equations
zbMATH Keywords: resonance
MaRDI profile type: Publication
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OpenAlex ID: W2059233704
description: scientific article; zbMATH DE number 6152197