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Three solutions for a nonlocal problem with critical growth
Authors:Natalí Ailín Cantizano  Analía Silva
Institution:Instituto de Matemática Aplicada San Luis, IMASL, Universidad Nacional de San Luis and CONICET, Ejercito de los Andes 950, D5700HHW San Luis, Argentina
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=|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?=npn?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].
Keywords:Sobolev embedding  Non-local  Critical exponents  Concentration compactness
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