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 (−∆p) s u = |u| p * s −2 u + λf (x, u) in a bounded domain with Dirichlet condition, where (−∆p) s is the well known pfractional Laplacian and p * s = 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].
In this paper we give sufficient conditions to obtain continuity results of solutions for the so called ϕ-Laplacian Δ
ϕ
with respect to domain perturbations. We point out that this kind of results can be extended to a more general class of operators including, for instance, nonlocal nonstandard growth type operators.
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