Superlinear indefinite elliptic problems and Pohozyaev type identities
type: Item
instance of: scholarly article
title: Superlinear indefinite elliptic problems and Pohozyaev type identities
zbMATH Open document ID: 0937.35060
author: Miguel Ramos
author: Susanna Terracini
author: Christophe Troestler
published in: Journal of Functional Analysis
publication date: 2000-05-29T00:00:00Z
review text: In this paper one seeks nonzero solutions for the Dirichlet problem \(-\Delta u=\mu u+a(x)g(u),\) \(u\in H^1_0(\Omega)\), where \(\Omega\) is a bounded domain in \(\text{ I R}^N\), \(\mu>0\), \(a\in C^2(\overline\Omega)\) changes sign in \(\Omega\) and \(g\) is superlinear both at zero and at infinity. Under a hypothesis implying that the zero set \(\Omega^0=\{x\in\overline\Omega:a(x)=0\}\) has Lebesgue measure zero, the authors prove that the above problem has a nonzero solution.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1268058
zbMATH Keywords: existence
zbMATH Keywords: superlinear
MaRDI profile type: Publication
full work available at URL: jfan.1998.3332
OpenAlex ID: W1992716963
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DOI: 10.1006/JFAN.1998.3332
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description: scientific article; zbMATH DE number 1268058