Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2002-12-31
Some Remarks on Complementarity Problems in a Hilbert SpaceAntonio Carbone and P. P. Zabrejko (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