English

Three solutions for a nonlocal problem with critical growth

Analysis of PDEs 2018-05-01 v1

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 (Δp)su=ups2u+λf(x,u)(-\Delta_p)^s u= |u|^{p^{*}_s -2} u +\lambda f(x,u) in a bounded domain with Dirichlet condition, where (Δp)s(-\Delta_p)^s is the well known pp-fractional Laplacian and ps=npnspp^*_s=\frac{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 pp-fractional Laplacian and Ekeland's variational Principle.

Keywords

Cite

@article{arxiv.1804.10699,
  title  = {Three solutions for a nonlocal problem with critical growth},
  author = {Natalí Ailín Cantizano and Analía Silva},
  journal= {arXiv preprint arXiv:1804.10699},
  year   = {2018}
}

Comments

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

R2 v1 2026-06-23T01:38:40.809Z