Topological Degree for Maximal Monotone Operators and Application to Parametric Optimization Problems

The generalized topological degree theory is based on the Brouwer and Leray-Schauder degrees. It can be defined for general classes of mappings. The purpose of this article is two-fold. One goal is to define the topological degree for maximal monotone operators. Particular attention is paid to the continuation methods for this kind of operators and real functions of convex type. This allows us to extend some recent results (see [5], [6]) by withdrawing the compactness assumptions.