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

Athanassios G. Kartsatos and Igor V. Skrypnik

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Abstract

Let X be an infinite-dimensional real reflexive Banach space with dual space X and GX open and bounded. Assume that X and X are locally uniformly convex. Let T:XD(T)2X be maximal monotone and C:XD(C)X quasibounded and of type (S˜+). Assume that LD(C), where L is a dense subspace of X, and 0T(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


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