Existence and multiplicity results for resonant fractional boundary value problems

IANNIZZOTTO, ANTONIO;Papageorgiou, Nikolaos S.

2018-01-01

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Abstract

We study a Dirichlet-type boundary value problem for a pseudo- di↵erential equation driven by the fractional Laplacian, with a non-linear reac- tion term which is resonant at infinity between two non-principal eigenvalues: for such equation we prove existence of a non-trivial solution. Under further assumptions on the behavior of the reaction at zero, we detect at least three non-trivial solutions (one positive, one negative, and one of undetermined sign). All results are based on the properties of weighted fractional eigenvalues, and on Morse theory.