Periodic solutions for a class of perturbed fifth-order autonomous differential equations via averaging theory

Document Type : Research Paper


Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, Annaba, 23000, Algeria


In this work, we use the averaging theory of first order to study the periodic solutions of the perturbed fifth-order autonomous differential equation
x^{(5)}- \lambda \ddddot{x}+(p^{2}+1) \dddot{x}-\lambda(p^{2}+1)\ddot{x}+p^{2}\dot{x}-\lambda p^{2}x= \varepsilon F(x,\dot{x}, \ddot{x}, \dddot{x}, \ddddot{x}),
where $\lambda ,$ and $\varepsilon $ are real parameters, $p$ is rational number different from $-1,$ $0,$ $1$, $\varepsilon $ is a small enough and $F\in C^2 $ is a nonlinear autonomous function. we present some applications to illustrate our main results.


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Volume 13, Issue 2
July 2022
Pages 2479-2491
  • Receive Date: 28 February 2022
  • Revise Date: 21 June 2022
  • Accept Date: 03 July 2022