On the uniqueness of the Browder degree

Abstract

We consider the topological degree theory for maximal monotone perturbations of mappings of class (S + ) originally introduced by F. Browder in 1983. In the original construction it is implicitly assumed that the maximal monotone part is at least densely defined. The construction itself remains valid without this assumption. However, for the proof of the uniqueness of the degree the assumption is crucial. We shall recall the construction of the degree and show how the stabilization of the degree can be obtained directly, thus avoiding a series of technical lemmas used by F. Browder. The main result of this paper is the proof for the uniqueness of the degree in the general case. We also discuss the class of admissible homotopies, which may be quite narrow in case the domain of the maximal monotone part is not densely defined.