Kasyanov P. Differential-operator inclusions and multivariation inequalities in infinitedimensional spaces with pseudomonotone type maps

We study differential-operator inclusions in Banach spaces with -quasimonotone maps. We justify the Faedo-Galerkin method and the method of finite differences for a resolvability for the given objects under the weakened -coercive condition, -quasimonotony and quasiboundedness condition. The important a priori estimates are obtained. It is proved, that the class of maps with semibounded variation swallows the class of semimonotone multivalued maps, introduced by Vainberg. The class of multivalued maps, under consideration, forms a convex cone in a class . We investigate the base properties of subdifferential maps and variation inequality in Frechet spaces. For a special class of irreflexive spaces of distributions with integrable derivatives we prove a series of theorems about a continuity and compactness embedding.