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This paper is devoted to the study of periodic solutions for a radiallysymmetric semilinear wave equation in an $n$-dimensional ball. By combining thevariational methods and saddle point reduction technique, we prove there existat least three periodic solutions for arbitrary space dimension $n$. Thestructure of the spectrum of the linearized problem plays an essential role inthe proof, and the construction of a suitable working space is devised toovercome the restriction of space dimension.

Existence of multiple periodic solutions for a semilinear wave equation in an $n$-dimensional ball