Museyko O. Limit analysis of variational inequalities with parameter

The object of research is variational inequality with small parameter. The purpose is to introduce the unified procedure for homogenization of wide class of variational inequalities, propose mathematical basis for limit variational inequalities construction, establish sufficient conditions when there exists the only homogenized inequality and point out its main variational properties. Methods: functional analysis, concept of S-convergence for extremal problems, G- and G*-convergence of operators. Results allows to construct homogenized variational inequality, which is simple to solve comparatively to original inequality with parameter, which is hard or impossible to solve. For the perforated domain problems the structure of homogenized variational inequality is obtained. Field is mathematical problems with small parameter.