Existence and multiplicity results for resonant fractional boundary value problems

Antonio Iannizzotto; Nikolaos S. Papageorgiou

doi:10.3934/dcdss.2018028

Article Contents

2018, Volume 11, Issue 3: 511-532. Doi: 10.3934/dcdss.2018028

This issue Previous Article Some remarks on boundary operators of Bessel extensions Next Article Multiple solutions of fractional Kirchhoff equations involving a critical nonlinearity

Existence and multiplicity results for resonant fractional boundary value problems

Antonio Iannizzotto^1, , and
Nikolaos S. Papageorgiou^2,

1.
Department of Mathematics and Computer Science, University of Cagliari, Viale L. Merello 92, 09123 Cagliari, Italy
2.
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece

* Corresponding author: A. Iannizzotto.
* Corresponding author: A. Iannizzotto.

Received: May 2017

Revised: August 2017

Published: June 2018

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Abstract

We study a Dirichlet-type boundary value problem for a pseudo-differential equation driven by the fractional Laplacian, with a non-linear reaction 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.

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Mathematics Subject Classification: Primary: 35R11, 35P05; Secondary: 49F15.

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