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