Kasyanov P. Differential-operator inclusions in Banach spaces with w lambda 0-pseudomonotone maps.

We study differential-operator inclusions in Banach spaces with w lambda 0-pseudomonotone maps. We justify the Faedo-Galerkin method and the method of singular per-turbations for a resolvability for the given objects under the weakened + - -coercive condition, w lambda 0-pseudomonotony and quasiboundedness condition. The important a priori estimates are obtained. We investigate the base properties of subdifferential maps and variation inequality in Frechet spaces. The sufficient conditions of upper semicontinuoty for local subdifferential map and boundness for subdifferential map of main convex lower semicontinuous function in Frechet space are applied. Theorem about boundness of subdifferential map is novice even in Banach spaces. Generous Weierstrass theorem for Frechet spaces is proved. For a special class of irreflexive spaces of distributions with integrable derivatives we prove a series of theorems about a continuity and compactness embedding.