Three nontrivial solutions for nonlinear fractional Laplacian equations

2016/04/18 by Düzgün, Fatma Gamze, Iannizzotto, Antonio · 1 citation
Mathematics · #35P30 #35R11 #49F15 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35P30 #msc:35R11 #msc:49F15

paper · pdf · doi:10.48550/arxiv.1604.05185

15 pages

Abstract

We study a Dirichlet-type boundary value problem for a pseudodifferential equation driven by the fractional Laplacian, proving the existence of three nonzero solutions. When the reaction term is sublinear at infinity, we apply the second deformation theorem and spectral theory. When the reaction term is superlinear at infinity, we apply the mountain pass theorem and Morse theory.

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