Abstract
We consider the existence of weak solutions of the periodic-Dirichlet problem on ]0, 2π[×]0, π[for the semi-linear wave equation u tt -uv xx -f(t, x, u=0 when x(t, x)⩽lim in u −1 f(t, x, u)⩽lim supu −1 f(t, x, u) ⩽ Β(t, x ¦u¦→∞ ¦u¦→∞ and α and Β satisfy some nonresonance conditions of non uniform type withr espect to two consecutive nonzero eigenvalues of the associated linear problem. The proof is based upon one generalized continuation theorem for some perturbations of mappings which are not of Fredholm type.
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