Abstract and Applied Analysis
Volume 2005 (2005), Issue 2, Pages 121-158
doi:10.1155/AAA.2005.121
A new topological degree theory for densely defined quasibounded (S˜+)-perturbations of multivalued maximal monotone operators in reflexive Banach spaces
1Department of Mathematics, University of South Florida, Tampa 33620-5700, FL, USA
2Institute for Applied Mathematics and Mechanics, National Academy of Science of Ukraine, R. Luxemburg Street 74, Donetsk 83114, Ukraine
Received 24 March 2004
Copyright © 2005 Athanassios G. Kartsatos and Igor V. Skrypnik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let X be an infinite-dimensional real reflexive Banach
space with dual space X∗ and G⊂X open and bounded. Assume that X and X∗ are locally uniformly
convex. Let T:X⊃D(T)→2X∗ be maximal
monotone and C:X⊃D(C)→X∗ quasibounded and of
type (S˜+). Assume that L⊂D(C),
where L is a dense subspace of X, and 0∈T(0). A
new topological degree theory is introduced for the sum T+C. Browder's degree theory has thus been extended to
densely defined perturbations of maximal monotone operators
while results of Browder and Hess have been extended to
various classes of single-valued densely defined generalized
pseudomonotone perturbations C. Although the main results
are of theoretical nature, possible applications of the new
degree theory are given for several other theoretical
problems in nonlinear functional analysis.