




Volume 35 • Number 1 • 2012 

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Existence of Periodic Solutions of $p(t)$Laplacian Systems
Liang Zhang and Yi Chen
Abstract.
In this paper, by using the least action principle in critical point theory, we obtain some existence theorems of periodic solutions for $p(t)$Laplacian system
\begin{equation*}
\left\{
\begin{aligned}
&\frac{d}{dt}(\dot{u}(t)^{p(t)2}\dot{u}(t))=\nabla F(t,u(t))\quad
\text{a.e. }t\in[0,T] \\
&u(0)u(T)=\dot{u}(0)\dot{u}(T)=0,
\end{aligned}
\right.
\end{equation*} which generalize some existence theorems.
2010 Mathematics Subject Classification: 34C25, 35A15.
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