Multiple positive solutions for a Schrödinger-Poisson-Slater system

2009/05/14 by Gaetano Siciliano, Siciliano, Gaetano
Mathematics · #35J50 #55M30 #74G35 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J50 #msc:55M30 #msc:74G35

paper · pdf · doi:10.48550/arxiv.0905.2358

added references and improved the result

arxiv created 2009/06/22 · arxiv updated 2009/12/01

Abstract

In this paper we investigate the existence of positive solutions to the following Schrödinger-Poisson-Slater system [c]ll - Δu+ u + λϕu=|u|^p-2u & in Ω-Δϕ= u² & in Ωu=ϕ=0 & on ∂Ω. where Ω is a bounded domain in R³,λ is a fixed positive parameter and p<2^*=(2N)/(N-2). We prove that if p is "near" the critical Sobolev exponent 2^*, then the number of positive solutions is greater then the Ljusternik-Schnirelmann category of Ω.

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