Positive solutions to a fourth-order elliptic problem by the Lusternik–Schnirelmann category

In this paper we consider the fourth-order problem{Δ2u=μ|u|s−1u+|u|2⁎−2uinΩ,u,−Δu>0in Ω,u,Δu=0on ∂Ω, where Ω is a smooth bounded domain in RN, N≥5 and 2⁎=2N/(N−4). We assume 2≤s+1

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2014-12, Vol.420 (1), p.532-550
Main Authors: Melo, Jéssyca Lange Ferreira, Moreira dos Santos, Ederson
Format: Article
Language:English
Subjects:
Biharmonic equation
Critical exponent
Lusternik–Schnirelmann category
Positive solutions
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Summary:In this paper we consider the fourth-order problem{Δ2u=μ|u|s−1u+|u|2⁎−2uinΩ,u,−Δu>0in Ω,u,Δu=0on ∂Ω, where Ω is a smooth bounded domain in RN, N≥5 and 2⁎=2N/(N−4). We assume 2≤s+1
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2014.05.084