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Zeitschrift für Analysis und ihre Anwendungen


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Volume 22, Issue 1, 2003, pp. 33–42
DOI: 10.4171/ZAA/1130

Published online: 2003-03-31

Explicit and Implicit Complementarity Problems in a Hilbert Space

Antonio Carbone[1] and P. P. Zabrejko[2]

(1) Università della Calabria, Arcavacata Di Rende, Italy
(2) The Academy of Sciences of Belarus, Minsk, Belarus

We present some new results about solvability of implicit complementarity 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.

Keywords: Explicit and implicit complementarity problems, topological degree, exceptional elements, homotopy, operators of class S+, quasi-monotono operators

Carbone Antonio, Zabrejko P. P.: Explicit and Implicit Complementarity Problems in a Hilbert Space. Z. Anal. Anwend. 22 (2003), 33-42. doi: 10.4171/ZAA/1130