Periodic solutions for nonlocal fractional equations

TL;DR

This paper establishes the existence of multiple weak periodic solutions for nonlocal fractional equations with periodic boundary conditions using variational methods and critical point theory.

Contribution

It introduces new results on the existence of multiple periodic solutions for nonlocal fractional equations employing advanced variational techniques.

Findings

Proved the existence of at least two periodic solutions.

Applied critical point theory to nonlocal fractional equations.

Results are novel in the context of these equations.

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.