Multiple positive solutions for semilinear elliptic equations in \(\mathbb R^N\) involving concave-convex nonlinearities and sign-changing weight functions
type: Item
instance of: scholarly article
title: Multiple positive solutions for semilinear elliptic equations in \(\mathbb R^N\) involving concave-convex nonlinearities and sign-changing weight functions
zbMATH Open document ID: 1387.35309
DOI: 10.1155/2010/658397
author: Tsing-San Hsu
author: Huei-Li Lin
published in: Abstract and Applied Analysis
publication date: 2010-09-27T00:00:00Z
review text: Summary: We study the existence and multiplicity of positive solutions to the semilinear elliptic equation \[ -\Delta u+u=\lambda a(x)|u|^{q-2}u+b(x)|u|^{p-2}u \;\text{ in } {\mathbb R}^N, \;\;u\in H^1({\mathbb R}^N), \] where \(\lambda>0\), \(1<q<2<p<2^*\) \((2^*=2N/(N-2))\) if \(N\geq3\), \(2^*=\infty\) if \(N=1,2\), \(a(x)\), \(b(x)\) satisfy suitable conditions, and \(a(x)\) may change sign in \({\mathbb R}^N\).
Mathematics Subject Classification ID: 35J91
Mathematics Subject Classification ID: 35J20
zbMATH DE Number: 5791633
Wikidata QID: Q58649895
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2010/658397
OpenAlex ID: W2067288797
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description: scientific article; zbMATH DE number 5791633