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.

Existence and multiplicity results for resonant fractional boundary value problems

IANNIZZOTTO, ANTONIO;
2018-01-01

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.
2018
Fractional Laplacian; Eigenvalue problems; Morse theory
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/225959
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