On The Existence of Periodic Solutions for a Certain System of Third Order Nonlinear Differential Equations

TL;DR

This paper investigates conditions under which periodic solutions exist for a broad class of third-order nonlinear vector differential equations, providing theoretical guarantees and illustrative examples.

Contribution

It establishes sufficient conditions for the existence and uniqueness of periodic solutions in a general third-order nonlinear vector differential equation.

Findings

Derived new sufficient conditions for periodic solutions

Proved uniqueness under certain conditions

Provided an illustrative example

Abstract

In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite general third- order nonlinear vector differential equation, and one example is given for illustration of the subject.