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 in a bounded domain with Dirichlet condition, where is the well known -fractional Laplacian and is the critical Sobolev exponent for the non local case. The proof is based in the extension of the Concentration Compactness Principle for the -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