Abstract

This study aims to provide sufficient conditions for the existence of periodic solutions of the fifth-order differential equation.Design/methodology/approachThe authors shall use the averaging theory, more precisely Theorem $6$.FindingsThe 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/valueIn this article, the authors provide sufficient conditions for the existence of periodic solutions of the fifth-order differential equation.