Infinitely many periodic solutions for a class of fractional Kirchhoff problems

TL;DR

This paper establishes the existence of infinitely many nontrivial periodic solutions for a class of fractional Kirchhoff problems involving a relativistic Schrödinger operator, broadening understanding of nonlinear fractional PDEs.

Contribution

It introduces new methods to prove the existence of infinitely many solutions for fractional Kirchhoff problems with relativistic operators and various nonlinearities.

Findings

Existence of infinitely many solutions proven

Solutions are nontrivial and weak

Applicable to problems with different nonlinearities

Abstract

We prove the existence of infinitely many nontrivial weak periodic solutions for a class of fractional Kirchhoff problems driven by a relativistic Schr\"odinger operator with periodic boundary conditions and involving different types of nonlinearities.