Application of local linking to asymptotically linear wave equations with resonance II

Existence of a time-periodic solution to a non-linear wave equation with resonance is established by a variational method.We consider the 2periodic weak solution to a wave equation 2u(x, t) = h(x, t, u(x, t)) of space dimension 1, where h(x, t, ) is asymptotically linear in both as 0 or , with the co-efficient as belonging to (2).It was proved that there are some cases, where the difference of h(t, x, ) from its linear approximation is not bounded, that guarantee the existence of a non-trivial weak solution.In this paper, we show that the restriction in our previous result imposed on these co-efficients can be further relaxed.