Degree Theory for Variational Inequalities in Complementary Systems

Abstract

Working out degree theory for the investigation of finite-dimensional variational inequalities with continuous mappings in the usual way. All properties typical for a topologiocal degree are proved. Then the $K$-degree is generalized by the Galerkin procedure for some class $S_A(X)$ of monotone-like operators in complementary systems. On the basis of our theory some new results concerning solvability of variational inequalities in complementary systems are proved. These results make it possible to obtain new facts on solvability of variational inequalities as well as operator equations with stongly nonlinear differential operators.