ON THE LIMIT CYCLES FOR A CLASS OF FOURTH-ORDER DIFFERENTIAL EQUATIONS

Amel Boulfoul, Amar Makhlouf

Abstract


We provide sufficient conditions for the existence of periodic solutions of the fourth-order differential equation

\begin{equation*}

\ddddot{x}+(1+p^{2})\ddot{x}+p^{2}x=\epsilon F(t,x,\dot{x},\ddot{x},\dddot{x}),

\end{equation*}

where $p=p_{1}/p_{2}$ with $p_{1},p_{2}\in \mathbb{N}$ and $p$ is different from $-1,0,1.$ $\epsilon$ is a small real parameter, and $F$ is a non-autonomous periodic function with respect to $t$.


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