A nonlinear periodic averaging principle. (Q1406787)

In a Hilbert space, a class of second-order evolution inclusions with an \(m\)-dissipative operator of special kind and a multivalued perturbation is considered. The perturbation is upper semicontinuous with compact convex values. Under assumptions on the perturbation expressed in terms of measure of noncompactness, an existence theorem and a nonlinear averaging principle for periodic solutions are established. This result supplements the nonlinear averaging principle worked out in previous works of the authors.