A new topological degree theory for perturbations of the sum of two maximal monotone operators (Q550211)

The paper is devoted to the construction of a new topological degree \(d (T + S + C, G, 0)\) for operators in a real reflexive Banach space, where \(T\) is a maximal monotone and strongly quasibounded mapping, \(S\) is a maximal monotone mapping, and \(C\) is quasibounded with respect to \(S\) and satisfies a generalized \((S_ {+})\)-condition with respect to \(S\). This topological degree theory is based on the Kartsatos-Skrypnik degree theory that was recently developed by the second author and \textit{J. Quarcoo} [Nonlinear Anal., Theory Methods Appl. 69, No.~8, A, 2339--2354 (2008; Zbl 1158.47045)].