| Contents |
| We consider the following nonlinear wave equation:
$$
(1) \quad \left\{
\begin{array}{lc}
\omega^2 u_{tt} -u_{xx} +\varepsilon f(x,u)=0 \
\hbox{in} \ (x,t)\in (0,\pi) \times \mathbb{R},\\
u(x,t)=u(x,t+2\pi).
\end{array}\right.
$$
We are interested in the case $\omega\in \mathbb{R} \setminus \mathbb{Q}$, $f(x,0)=f_s(x,0)=0$ and $f(x,s)$ has a superlinear growth at infinity.
In this talk, we discuss the existence of nontrivial periodic solutions of (1) under Dirichlet boundary condition. We also study the existence of spatially non-constant periodic solutions of the orresponding free vibration problem. |
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