Minimal periods of semilinear evolution equations with Lipschitz nonlinearity revisited

TL;DR

This paper establishes a lower bound on the period of periodic solutions for semilinear evolution equations with Lipschitz nonlinearities, extending previous results to a broader class of nonlinear terms.

Contribution

It provides a new lower bound for the period of solutions that depends on the Lipschitz constant and applies to the full range of nonlinearities compatible with local existence theory.

Findings

Lower bound depends on Lipschitz constant and fractional power domain

Applicable to the full range of nonlinear terms with local existence

Extends previous period bounds to more general nonlinearities

Abstract

We obtain a lower bound for the period of periodic solutions of semilinear evolution equations for the full range of nonlinear terms for which standard local existence theory applies. This lower bound depends on the Lipschitz constant of the nonlinear term as an operator acting on the domain of a fractional power of the linear operator into the base space.