Let X be a real Banach space, A : D(A) ⊆ X ; X an m-accretive operator and F : R × D(A) ; X a multi-function which is 2π -periodic with respect to its first argument, has nonempty, closed, convex and weakly compact values and is strongly-weakly upper semicontinuous. In this paper we prove the existence of at least one solution for the problemin the case in which F satisfies an appropriate "sign" condition.
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