Generalizations of browder’s degree theory

Abstract

The starting point of this paper is the recent important work of F. E. Browder, who extended degree theory to operators of monotone type. The degree function of Browder is generalized to maps of the form T+f+G, where T is maximal monotone, f is of class (S)+bounded, and G(•) is an u.s.c. compact multifunction. It is also generalized to maps of the form f+NG, with f of class (S)+and NGthe Nemitsky operator of a multifunction G(x, r) satisfying various types of sign conditions. Some examples are also included to illustrate the abstract results.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1090/S0002-9947-1995-1284911-6

Keywords

Additivity on domain, Approximate selector, Compact embedding, Degree function, Homotopy invariance, Monotone operator, Multifunction, Nemitsky operator, Normalization, Operator of class (S) +, Sign condition

Publication Date

1-1-1995

Journal Title

Transactions of the American Mathematical Society

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