About One Class of Operators Inclusions

The operator inclusion $0\in A(x) + N(x)$ is studied. The main results refer to the case, when $A$ – a bounded operator of monotone type from a reflexive space into conjugate to it, $N$ – a conevalued operator. No solution criterion of the viewed inclusion is set up. Integer characteristics of multivalued mappings with homotopy invariance and additivity are introduced. Application to the theory of variational inequalities with multivalued operators is identified.