Existence of solutions for an elliptic equation with indefinite weight
type: Item
instance of: scholarly article
title: Existence of solutions for an elliptic equation with indefinite weight
zbMATH Open document ID: 1143.35043
author: Zeng Jing
author: Li Yongqing
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-04-26T00:00:00Z
review text: The authors deal with the existence of solutions of the following elliptic equation: \[ -\Delta_x u= V(x)u+ f(x,u),\quad u\in H^1(\mathbb{R}^N),\tag{1} \] where \(V(x)\) is a function with possibly changing sign, \(f\) is a continuous function on \(\mathbb{R}^N\times \mathbb{R}\). Under appropriate assumptions on \(f(x,u)\), the existence of \(m-n\) pairs of nontrivial solutions (\(m> n\), \(m\) and \(n\) are integers) of (1) is proved. There are two main difficulties in considering (1): a) loss of compactness; b) since \(V(x)\) may change sign, it leads to difficulty in verifying the Palais-Smale condition.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B38
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 5146764
zbMATH Keywords: critical-point theory
zbMATH Keywords: elliptic equation
zbMATH Keywords: indefinite weight
zbMATH Keywords: Palais-Smale condition
MaRDI profile type: Publication
full work available at URL: j.na.2006.03.034
OpenAlex ID: W2033750537
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DOI: 10.1016/J.NA.2006.03.034
description: scientific article; zbMATH DE number 5146764