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Published in:
2020 | OriginalPaper | Chapter
17. Radially Symmetric Wave Equations
Author : Martin Schechter
Published in: Critical Point Theory
Publisher: Springer International Publishing
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Abstract
In this chapter we study periodic solutions of the Dirichlet problem for the semilinear wave equation where
$$\displaystyle \square u:= u_{tt}-\Delta u = f(t,x,u),\quad t\in {\mathbb R},\quad x\in \mathcal B_R, $$
$$\displaystyle u(t,x) = 0,\quad t\in {\mathbb R},\quad x\in \partial \mathcal B_R, $$
$$\displaystyle u(t+T,x) = u(t,x),\quad t\in {\mathbb R},\quad x\in \mathcal B_R, $$
$$\displaystyle \mathcal B_R = \{x\in {\mathbb R}^n:|x|<R\}. $$