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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.

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