Existence of infinitely many periodic solutions for the radially symmetric wave equation with resonance

In this paper, we consider the periodic-Dirichlet problem for a forced nonlinear wave equation with resonance utt−Δu=μu+a(t,x)|u|p−1uutt−Δu=μu+a(t,x)|u|p−1u in a n-dimensional ball. Under some suitable assumptions on μ, p   and a(t,x)a(t,x), we prove the existence of infinitely many radially symmetric time-periodic solutions for the problem by variational methods.