Work

On the Periodic Orbits of Continuous Third-order Differential Equation With Piecewise Perturbations

Year: 2025

Type: article

Abstract: In this paper, we study the sufficient conditions for the existence of periodic solutions of the following differential equation $ \begin{equation*} \dddot{x}=-\dot{x}+\varepsilon |\ddot{x}|-\varepsilon \left( \alpha x-\beta \dot{x}\right) ^{m}, \end{equation*} $ where $ m $ is a natural number, and $ \alpha $, $ \beta $ and $ \varepsilon $ are real parameters with $ |\varepsilon|>0 $ being small. We apply the averaging method and the Melnikov function method respectively to study the periodic solutions of this type of differential equation. We also provide an example as an application.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20240522

Authors: Zouhair Diab, Feng Li, Meilan Cai

Institutions: Université Larbi Tébessi, Linyi University

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shandong Province

Awards: G1299771763, G2958008424, G6326006225, G7681730333