SemilinNonlinear wave equation

A general nonlinear wave equation can be expressed as

\begin{displaymath} (NWE) \;\; \left \{ \begin{array}{ll} u_{tt}-u_{xx}= f(x,t... ...=u(\pi,t)=0 &\, \forall t \in \mathbb{R} \end{array} \right. \end{displaymath}


where $f(x,t,s)$ is a continuous, monotonic increasing or decreasing (in $s$) real function on $[0,\pi]\times {\mathbb{R}}^2 $ and $2\pi$-periodic in $t$. Nontrivial periodic solutions are of interest in many applications. Existence of multiple or even infinitely many periodic solutions to some special cases of (NWE), e.g., $f(x,t,s)$ is superlinear in $s$ and/or independent of the time $t$, have been proved by many authors such as P. Rabinowitz, V. Benci, M. Berti, etc.




Owned by X. Chen

Oct-13-2006