Boundary value problem with fractional p-Laplacian operator

2014/12/19 by César Torres, Torres, César
Mathematics · #26A33 #58E05 #65L10 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:26A33 #msc:58E05 #msc:65L10

paper · pdf · doi:10.48550/arxiv.1412.6438

arxiv created 2014/12/19 · arxiv updated 2014/12/22

Abstract

The aim of this paper is to obtain the existence of solution for the fractional p-Laplacian Dirichlet problem with mixed derivatives _tD_T^α(|₀D_t^αu(t))|^p-2₀D_t^αu(t)) = f(t,u(t)), t∈ [0,T],
u(0) = u(T) = 0, where (1)/(p) < α<1, 1<p<∞ and f:[0,T]× ℝ → ℝ is a Carathéodory function wich satisfies some growth conditions. We obtain the existence of nontrivial solution by using the Mountain Pass Theorem.

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