Andreev M.V.

Variation inequalities and evolution inclusions in Banach spaces with wλ0 – pseudo-monotone maps are investigated. The Faedo–Galerkin method and the method of finite differences for the resolvability for the given objects under the weakened +- coercive condition, wλ0 – pseudo-monotony, quasi-boundedness and condition Sk are based. The important a priory estimated are obtained. It is proved, that the class of maps with semi-bounded variation swallows the class of semi-monotone multi-valued maps. The class of multi-valued maps, under consideration, forms a convex cone in a class B(X;X*).

The new methods of building strategies of imperfect inspections problems for successfully disclose of the disorder and the design of experiments with multi-alternatives are developed. Necessary and sufficient conditions are developed if the failure distribution is known explicitly, whereas a sufficient condition is given if only the increasing failure intensity is known from experiment.