Explicit and Implicit Complementarity Problems in a Hilbert Space | Zendy

Antonio Carbone | Zendy; Petr P. Zabrejko | Zendy

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Explicit and Implicit Complementarity Problems in a Hilbert Space

Author(s) -

Antonio Carbone,

Petr P. Zabrejko

Publication year - 2003

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1130

Subject(s) - complementarity (molecular biology) , hilbert space , mathematics , pure mathematics , rigged hilbert space , space (punctuation) , mathematical economics , algebra over a field , computer science , reproducing kernel hilbert space , genetics , biology , operating system

We present some new results about solvability of implicit complementar- ity problems in a Hilbert space. We discuss two approaches. One of them is based on the usual change of variables and reduces the implicit complementarity problem to the explicit one. The second approach is based on the Skrypnik degree which, in the case of mappings in a Hilbert space, is essentially more general in comparison with the classical Leray-Schauder degree. In both cases, the solvability results are formulated in terms of auxiliary complementarity problems with parameter.

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