Three solutions for a nonlocal problem with critical growth

2018/04/27 by Cantizano, Natalí Ailín, Silva, Analía · 1 citation
#35R01 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.10699

Abstract

The main goal of this work is to prove the existence of three different solutions (one positive, one negative and one with nonconstant sign) for the equation (-Δ_p)^s u= |u|^p^*_s -2 u +λf(x,u) in a bounded domain with Dirichlet condition, where (-Δ_p)^s is the well known p-fractional Laplacian and p^*_s=(np)/(n-sp) is the critical Sobolev exponent for the non local case. The proof is based in the extension of the Concentration Compactness Principle for the p-fractional Laplacian and Ekeland's variational Principle.

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