Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4612666 | Journal of Differential Equations | 2009 | 17 Pages |
Abstract
Let us consider the quasilinear problem(Pε){−εpΔpu+up−1=f(u)inΩ,u>0inΩ,u=0on∂Ω where Ω is a bounded domain in RNRN with smooth boundary, N>pN>p, 2⩽p
0ε>0 is a parameter. We prove that there exists ε∗>0ε∗>0 such that, for any ε∈]0,ε∗[ε∈]0,ε∗[, (Pε)(Pε) has at least 2P1(Ω)−12P1(Ω)−1 solutions, possibly counted with their multiplicities, where Pt(Ω)Pt(Ω) is the Poincaré polynomial of Ω. Using Morse techniques, we furnish an interpretation of the multiplicity of a solution, in terms of positive distinct solutions of a quasilinear equation on Ω , approximating (Pε)(Pε).
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Silvia Cingolani, Giuseppina Vannella,