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Degree theory for nonlinear mappings. (English) Zbl 0601.47050
Nonlinear functional analysis and its applications, Proc. Summer Res. Inst., Berkeley/Calif. 1983, Proc. Symp. Pure Math. 45, Pt. 1, 203-226 (1986).
[For the entire collection see Zbl 0583.00018.]
The author makes some remarks on the existence and uniqueness of the topological degree for various classes of nonlinear operators. Particular emphasize is taken on operators of monotone type which were first studied by G. J. Minty [see e.g. Duke Math. J. 29, 341-346 (1962; Zbl 0111.312)]. One should mention that there is a more elegant (i.e. not requiring Galerkin approximations) definition of degree which was recently proposed by V. Mŭstonen.
Reviewer: J.Appell

MSC:
47J05 Equations involving nonlinear operators (general)
47H10 Fixed-point theorems
47H05 Monotone operators and generalizations
58C30 Fixed-point theorems on manifolds
35J60 Nonlinear elliptic equations