| Abstract: |
| We study the generalized semilinear wave equation
$\begin{align*}
V(x) u_{tt} - d(t) M(x, \partial_{x} ) u - V(x) |u|^{p-1} u=0 \quad \text{ for } \quad (x,t) \in \mathbb{R}^N \times \mathbb{R}
\end{align*}$
where $M$ is elliptic and $d$ is a positive potential. Our goal is to construct
solutions which are localized in space and/or time by means of variational
methods. We present our approach with its main difficulties and discuss suitable examples
for $M$ and $d$. This is joint work with Sebastian Ohrem and Wolfgang Reichel. |
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