## Abstract and Applied Analysis

### A new topological degree theory for densely defined quasibounded $({\widetilde{S}}_{+})$-perturbations of multivalued maximal monotone operators in reflexive Banach spaces

#### Abstract

Let $X$ be an infinite-dimensional real reflexive Banach space with dual space $X^*$ and $G\subset X$ open and bounded. Assume that $X$ and $X^*$ are locally uniformly convex. Let $T:X\supset D(T)\rightarrow 2^{X^*}$ be maximal monotone and $C:X\supset D(C)\rightarrow X^*$ quasibounded and of type $({\widetilde{S}}_{+})$. Assume that $L\subset D(C)$, where $L$ is a dense subspace of $X$, and $0\in T(0)$. 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2005, Number 2 (2005), 121-158.

Dates
First available in Project Euclid: 17 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1116340205

Digital Object Identifier
doi:10.1155/AAA.2005.121

Mathematical Reviews number (MathSciNet)
MR2179439

Zentralblatt MATH identifier
1110.47049

#### Citation

Kartsatos, Athanassios G.; Skrypnik, Igor V. A new topological degree theory for densely defined quasibounded $({\widetilde{S}}_{+})$-perturbations of multivalued maximal monotone operators in reflexive Banach spaces. Abstr. Appl. Anal. 2005 (2005), no. 2, 121--158. doi:10.1155/AAA.2005.121. https://projecteuclid.org/euclid.aaa/1116340205