This paper is devoted to the study of periodic solutions for a radially symmetric semilinear wave equation in an $n$-dimensional ball. By combining the variational methods and saddle point reduction technique, we prove there exist at least three periodic solutions for arbitrary space dimension $n$. The structure of the spectrum of the linearized problem plays an essential role in the proof, and the construction of a suitable working space is devised to overcome the restriction of space dimension.
Multiple periodic solutions for two classes of nonlinear difference systems involving classical $(φ_1,φ_2)$-Laplacian
Multiple periodic solutions for one-sided sublinear systems: A refinement of the Poincaré-Birkhoff approach
Existence of multiple periodic solutions to a semilinear wave equation with $x$-dependent coefficients
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