Topological degree for perturbations of linear maximal monotone mappings and applications to a class of parabolic problems. (English) Zbl 0806.47055

Berkovits, J.; Mustonen, V.

Rend. Mat. Appl., VII. Ser. 12, No. 3, 597-621 (1992).

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

Keywords:

topological degree; nonlinear parabolic initial-boundary value problems