Infinitely many solutions for p-Laplacian equation involving critical Sobolev growth

In this paper, we will prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth:−Δpu=|u|p⁎−2u+μ|u|p−2uin Ω,u=0on ∂Ω, provided N>p2+p, where Δp is the p-Laplacian operator, 1<p<N, p⁎=pNN−p, μ>0 and Ω is an open bounded domain in RN....

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Bibliographic Details
Published inJournal of functional analysis Vol. 262; no. 6; pp. 2861 - 2902
Main Authors Cao, Daomin, Peng, Shuangjie, Yan, Shusen
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.03.2012
Subjects
Critical Sobolev growth
Infinitely many solutions
p-Laplacian equations
Infinitely many solutions
p-Laplacian equations
Critical Sobolev growth
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Summary:In this paper, we will prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth:−Δpu=|u|p⁎−2u+μ|u|p−2uin Ω,u=0on ∂Ω, provided N>p2+p, where Δp is the p-Laplacian operator, 1<p<N, p⁎=pNN−p, μ>0 and Ω is an open bounded domain in RN.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2012.01.006