We consider the problem u_(tt) - u_(xx) + g(u) = f(x, t), 0 < x < π, t ∈ R, (1), u(0, t) - h_1u'_x(0, t) = 0, u(π, t) + h_2u'_x(π, t) = 0, t ∈ R, (2) u(x, t + T) = u(x, t), 0 < x < π, t ∈ R. (3) Here h_1, h_2 > 0, T = 2πa/b, where a and b are coprime positive integers, and f(x, t) is a given T-periodic function of t.
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