Chems Eddine Berrehail and Amar Makhlouf
The objective of this work is to study the periodic solutions for a class of sixth-order autonomous ordinary differential equations
Abstract
Purpose
The objective of this work is to study the periodic solutions for a class of sixth-order autonomous ordinary differential equations
Design/methodology/approach
The authors shall use the averaging theory to study the periodic solutions for a class of perturbed sixth-order autonomous differential equations (DEs). The averaging theory is a classical tool for the study of the dynamics of nonlinear differential systems with periodic forcing. The averaging theory has a long history that begins with the classical work of Lagrange and Laplace. The averaging theory is used to the study of periodic solutions for second and higher order DEs.
Findings
All the main results for the periodic solutions for a class of perturbed sixth-order autonomous DEs are presenting in the Theorem 1. The authors present some applications to illustrate the main results.
Originality/value
The authors studied Equation 1 which depends explicitly on the independent variable t. Here, the authors studied the autonomous case using a different approach.