Andreev M.V.

Methods of non-linear analysis and topological methods of variation inequalities and evolution inclusions

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*).

Non-linear methods for decisions making processes under uncertainty conditions

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.