Existence of a countable set of periodic, spherically symmetric solutions of a nonlinear wave equation

I. A. Kuzin


Abstract: Under suitable conditions countable solvability of the problem $-u_{tt}+\Delta u-g(u,r,t)=h(r,t)$ in $B_\pi$, $u(x,t)=u(x,t+T)$, $T>0$, $u(\partial B_\pi,t)=0$, where $B_\pi\subset\mathbf R^N$ is a ball of radius $\pi$, is proved.

UDC: 517.95

MSC: 35L05, 35L70

Received: 19.12.1989

 English version: Mathematics of the USSR-Izvestiya, 1992, 38:1, 107–129

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