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 T + f + G , where T T is maximal monotone, f f is of class ( S ) + {(S)_ + } bounded, and G ( ⋅ ) G( \cdot ) is an u.s.c. compact multifunction. It is also generalized to maps of the form f + N G f + {N_G} , with f f of class ( S ) + {(S)_ + } and N G {N_G} the Nemitsky operator of a multifunction G ( x , r ) G(x,r) satisfying various types of sign conditions. Some examples are also included to illustrate the abstract results.