Geodesic
Existence of a countable set of periodic, spherically symmetric solutions of a~nonlinear wave equation
Izvestiya. Mathematics , Tome 38 (1992) no. 1, pp. 107-129

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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. 
@article{IM2_1992_38_1_a4,
     author = {I. A. Kuzin},
     title = {Existence of a countable set of periodic, spherically symmetric solutions of a~nonlinear wave equation},
     journal = {Izvestiya. Mathematics },
     pages = {107--129},
     publisher = {mathdoc},
     volume = {38},
     number = {1},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a4/}
}
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I. A. Kuzin. Existence of a countable set of periodic, spherically symmetric solutions of a~nonlinear wave equation. Izvestiya. Mathematics , Tome 38 (1992) no. 1, pp. 107-129. http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a4/