| Abstract: |
| This talk is devoted to the existence of multiple time-periodic solutions for the nonlinear wave equation
$$u_{tt}- \triangle u = g(t,x,u)
$$
in an $n$-dimensional ball with radius $R$. An interesting feature is that the solvability of the problem depends on $n$, $R$ and the time-period $T$. Based on the spectral properties of the radially symmetric wave operator, we use the reduction arguments and variational methods to construct at least three radially symmetric solutions with time-period $T$, when $T$ is a rational multiple of $R$ and $g(t,x,u)$ satisfying some growth conditions. This is joint work with Zhitao Zhang. |
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