Periodic solutions for a class of fifth-order differential equations

Abstract

Purpose – This study aims to provide sufficient conditions for the existence of periodic solutions of the fifth-order differential equation. Design/methodology/approach – The authors shall use the averaging theory, more precisely Theorem $6$. Findings – The main results on the periodic solutions of the fifth-order differential equation (equation (1)) are given in the statement of Theorem 1 and 2. Originality/value – In this article, the authors provide sufficient conditions for the existence of periodic solutions of the fifth-order differential equation.

Keywords

• Periodic orbit
• Fifth-order differential equation
• Averaging theory