Three solutions for a nonlocal problem with critical growth

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

paper · pdf · doi:10.48550/arxiv.1804.10699

10 pages. arXiv admin note: text overlap with arXiv:0808.3143, arXiv:0912.3465

arxiv created 2018/04/27 · arxiv updated 2018/05/01

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.

Citations

• Multiple solutions for the p-laplace operator with critical growth
• Multiple solutions for the p(x)-laplace operator with critical growth

Cited by

• Brezis-Nirenberg type problem for fractional sub-Laplacian on the Heisenberg group

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