An Existence Theorem for Evolution Inclusions Involving Opposite Monotonicities

In this paper we examine evolution inclusions of the subdifferential type with the set-valued perturbation being nonconvex valued and dissipative. Under certain generally mild hypotheses on the data, we prove the existence of a strong global solution, extending earlier analogous results by M. Oˆtani and A. Cellina-V. Staicu. An example of a distributed parameter system is also presented in detail.