Infinitely many periodic solutions of a forced wave equation with an exponential growth nonlinear term

This paper is concerned with the nonlinear wave equation utt - uxx + g(u) = f(x, t), (x, t) ∈ (0, π) × R, u(0, t) = u(π, t) = 0, t ∈ R, u(x, t + 2π) = u(x, t), (x, t) ∈ (0, π) × R, where g is a continuous function with superlinear growth and f is a given function which is 2π-periodic in t and satisfies some symmetry condition. Using minimax methods, we prove the existence of infinitely many periodic solutions of the above equation provided that g possesses some exponential growth.