Three solutions for a nonlocal problem with critical growth - Cantizano, Natalí Ailín (2019)
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=|u|ps ⁎−2u+λf(x,u) in a bounded domain with Dirichlet condition, where (−Δp)s is the well known p-fractional Laplacian and ps ⁎=np / n−sp is the critical Sobolev exponent for the non local case. The proof follows the ideas of [28] and is based in the extension of the Concentration Compactness Principle for the p-fractional Laplacian [20] and Ekeland´s variational Principle [7].