Periodic solutions for nonlocal fractional equations

Vincenzo Ambrosio; Giovanni Molica Bisci

doi:10.3934/cpaa.2017016

Article Contents

2017, Volume 16, Issue 1: 331-344. Doi: 10.3934/cpaa.2017016

This issue Previous Article Struwe's decomposition for a polyharmonic operator on a compact Riemannian manifold with or without boundary Next Article Global well posedness for the ghost effect system

Periodic solutions for nonlocal fractional equations

Vincenzo Ambrosio^1, and
Giovanni Molica Bisci^2,

1.
Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Università degli Studi di Napoli Federico Ⅱ, via Cinthia, 80126 Napoli, Italy
2.
Dipartimento P.A.U. Università degli Studi Mediterranea di Reggio Calabria, Salita Melissari -Feo di Vito, 89100 Reggio Calabria, Italy

Author Bio: E-mail address: vincenzo.ambrosio2@unina.it; E-mail address: gmolica@unirc.it

Received: May 31, 2016

Revised: July 31, 2016

Published: January 2018

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Abstract

The purpose of this paper is to study the existence of (weak) periodic solutions for nonlocal fractional equations with periodic boundary conditions. These equations have a variational structure and, by applying a critical point result coming out from a classical Pucci-Serrin theorem in addition to a local minimum result for differentiable functionals due to Ricceri, we are able to prove the existence of at least two periodic solutions for the treated problems. As far as we know, all these results are new.

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Mathematics Subject Classification: Primary: 35A15; Secondary: 35B10, 35R11.

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