On minimal periods of solutions of higher order functional differential equations

TL;DR

This paper investigates the minimal periods of solutions to higher order functional differential equations, establishing their connection to the solvability of linear periodic problems and providing sharp bounds for these periods.

Contribution

It introduces new bounds for minimal periods of solutions and links the problem to the unique solvability of linear periodic differential equations.

Findings

Established a relationship between minimal periods and linear periodic problem solvability.

Derived sharp bounds for minimal periods of non-constant solutions.

Enhanced understanding of periodic solutions in higher order functional differential equations.

Abstract

We show that a problem on minimal periods of solutions of Lipschitz functional differential equations is closely related to the unique solvability of the periodic problem for linear functional differential equations. Sharp bounds for minimal periods of non-constant solutions of higher order functional differential equations with different Lipschitz nonlinearities are obtained.