On the Existence of Periodic Solutions of a ‎Certain‎‎ Fifth-order Autonomous Differential Equations  ‎via Topological Degree Theory

Bayat, Morteza

doi:10.22055/jamm.2023.42869.2133

On the Existence of Periodic Solutions of a ‎Certain‎‎ Fifth-order Autonomous Differential Equations ‎via Topological Degree Theory

Document Type : Original Paper

Author

Morteza Bayat

Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran

10.22055/jamm.2023.42869.2133

Abstract

In this paper, we study the existence of periodic solutions a certain

autonomous non-linear ordinary differential equations (ODE's) of‎ ‎fifth‎

order. Our method is based on the evaluation of Brouwer's degree

theory and making use of the homotopy invariance property of the

topological degree. Finally, we present some numerical results obtained by using the analytical methods.

Keywords

Periodic solutions

Topological Brouwer degree &lrm

theory&lrm

Homotopy invariance property

Rouch\`{e}'

s Theorem

Subjects