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Topological degree for perturbations of linear maximal monotone mappings and applications to a class of parabolic problems. (English) Zbl 0806.47055
Summary: We construct a topological degree for a class of mappings of the form \(F= L+ S\), where \(L\) is a closed densely defined maximal monotone operator and \(S\) is a nonlinear map of class \((S_ +)\) with respect to the domain of \(L\). The degree theory is then applied in the study of a class of nonlinear parabolic initial-boundary value problems.

47H11 Degree theory for nonlinear operators
47J05 Equations involving nonlinear operators (general)
35K30 Initial value problems for higher-order parabolic equations