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Zeitschrift für Analysis und ihre Anwendungen

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Volume 21, Issue 4, 2002, pp. 1005–1014
DOI: 10.4171/ZAA/1122

Published online: 2002-12-31

Some Remarks on 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 a new approach to the analysis of solvability properties for complementarity problems in a Hilbert space. This 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. Namely, the Skrypnik degree allows us to obtain some new results about solvability of complementarity problems in the infinite-dimensional case. The case of generalized solutions is also considered.

Keywords: Complementarity problems, topological degree, exceptional elements, homotopy, operator of class $S_+$, quasi-monotone operators

Carbone Antonio, Zabrejko P. P.: Some Remarks on Complementarity Problems in a Hilbert Space. Z. Anal. Anwend. 21 (2002), 1005-1014. doi: 10.4171/ZAA/1122