Further study on periodic solutions of elliptic equations with a fractional Laplacian

TL;DR

This paper establishes existence theorems for periodic solutions to linear and semilinear elliptic equations with fractional Laplacian, and provides bounds on periods, energy estimates, and related inequalities.

Contribution

It introduces new existence results and bounds for periodic solutions of fractional elliptic equations, along with energy and inequality estimates.

Findings

Existence theorems for periodic solutions to fractional elliptic equations.

Lower bounds on periods for semilinear fractional elliptic equations.

Energy estimates and inequalities for periodic solutions.

Abstract

We obtain some existence theorems for periodic solutions to several linear equations involving fractional Laplacian. We also prove that the lower bound of all periods for semilinear elliptic equations involving fractional Laplacian is not larger than some exact positive constant. Hamiltonian identity, Modica-type inequalities and an estimate of the energy for periodic solutions are also established.