On the degree theory for general mappings of monotone type ✩

Degree theory has been developed as a tool for checking the solution existence of nonlinear equations. In his classic paper published in 1983, Browder developed a degree theory for mappings of monotone type f +T , where f is a mapping of class (S)+ from a bounded open set Ω in a reflexive Banach space X into its dual X∗, and T is a maximal monotone mapping from X into X∗. This breakthrough paved the way for many applications of degree theoretic techniques to several large classes of nonlinear partial differential equations. In this paper we continue to develop the results of Browder on the degree theory for mappings of monotone type f +T . By enlarging the class of maximal monotone mappings and pseudo-monotone homotopies we obtain some new results of the degree theory for such mappings. © 2007 Elsevier Inc. All rights reserved