Existence and symmetry result for Fractional p-Laplacian in\n \ℝⁿ

2014/12/10 by Torres, César, César Torres
Mathematics · #Nonlinear Partial Differential Equations #Nonlinear Differential Equations Analysis #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.1412.3392

Abstract

In this article we are interested in the following fractional p-Laplacian\nequation in \ℝⁿ \amp;(-
Delta)_p
^alphau +\nV(x)u^p-2u = f(x,u)
mbox in
mathbbRⁿ, where p\≥\n2, 0< s < 1, n\≥ 2 and subcritical p-superlinear nonlinearity. By using\nmountain pass theorem with Cerami condition we prove the existence of\nnontrivial solution. Furthermore, we show that this solution is radially\nsimmetry.\n

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