ON THE PERIODIC ORBITS OF CONTINUOUS THIRD-ORDER DIFFERENTIAL EQUATION WITH PIECEWISE PERTURBATIONS

Zouhair Diab; Feng Li; Meilan Cai

doi:10.11948/20240522

2026 Volume 16 Issue 1

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Zouhair Diab, Feng Li, Meilan Cai. ON THE PERIODIC ORBITS OF CONTINUOUS THIRD-ORDER DIFFERENTIAL EQUATION WITH PIECEWISE PERTURBATIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 173-187. doi: 10.11948/20240522

Citation:

Zouhair Diab, Feng Li, Meilan Cai. ON THE PERIODIC ORBITS OF CONTINUOUS THIRD-ORDER DIFFERENTIAL EQUATION WITH PIECEWISE PERTURBATIONS[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 173-187. doi: 10.11948/20240522

ON THE PERIODIC ORBITS OF CONTINUOUS THIRD-ORDER DIFFERENTIAL EQUATION WITH PIECEWISE PERTURBATIONS

1.
Department of Mathematics, Echahid Cheikh Larbi Tebessi University, Tebessa 12002, Algeria
2.
School of Mathematics and Statistics, Linyi University, Linyi, Shandong 276000, China

Author Bio: Email: zouhair.diab@univ-tebessa.dz(Z. Diab); Email: lf0539@126.com(F. Li)
Corresponding author: Email: caimlmath@163.com(M. Cai)

Abstract

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.
- Averaging theory /
- Melnikov function /
- periodic solution
MSC: 34C29, 34C25, 37G15

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References

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