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The Semilinear Wave Equation

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Critical Point Theory

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Abstract

In this chapter we study periodic solutions of the Dirichlet problem for the semilinear wave equation:

$$\displaystyle \square u-\mu u:= u_{tt}- u_{rr} -\mu u = p(t,r,u),\quad t \in \mathbb R, \quad 0 <r < R, $$
$$\displaystyle u(t,R) = u(t,0) = 0, \quad t\in {\mathbb R}, $$
$$\displaystyle u(t+T,r) = u(t,r),\quad t\in {\mathbb R},\quad 0 \le r \le R. $$

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Authors and Affiliations

  1. Brooklyn, NY, USA

    Martin Schechter

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  1. Martin Schechter
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Schechter, M. (2020). The Semilinear Wave Equation. In: Critical Point Theory. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-45603-0_15

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