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arxiv: 1804.10699 · v1 · pith:ZHEX7M3Tnew · submitted 2018-04-27 · 🧮 math.AP

Three solutions for a nonlocal problem with critical growth

classification 🧮 math.AP
keywords criticaldeltafractionallaplacianprinciplesolutionsthreebounded
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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 $(-\Delta_p)^s u= |u|^{p^{*}_s -2} u +\lambda f(x,u)$ in a bounded domain with Dirichlet condition, where $(-\Delta_p)^s$ is the well known $p$-fractional Laplacian and $p^*_s=\frac{np}{n-sp}$ is the critical Sobolev exponent for the non local case. The proof is based in the extension of the Concentration Compactness Principle for the $p$-fractional Laplacian and Ekeland's variational Principle.

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