Periodic solutions of Nonsmooth Third-Order Differential Equations | ASJP

Journal of innovative applied mathematics and computational sciences
Volume 4, Numéro 1, Pages 1-10
2024-09-25

Periodic Solutions Of Nonsmooth Third-order Differential Equations

Authors : Rezaiki Nabil . Boulfoul Amel .

Abstract

In this paper, we study the existence of periodic solutions for the following piecewise third order differential equation $$ \dddot{x}+\dot{x}-\varepsilon\sum\limits_{i=1}^{2}c_i|x|^i=0, $$ with $\varepsilon$ a real parameter sufficiently small, $c_1$ and $c_2$ real numbers. By applying new results from the averaging theory for continuous differential systems, we prove the existence of at most one periodic solution for the differential equation. An example is given to illustrate the established result.

Keywords

Averaging theory ; Periodic Solutions ; Differential equations

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