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Zbl 1059.49015
Kassay, Gábor; Kolumbán, József; Páles, Zsolt
Factorization of Minty and Stampacchia variational inequality systems. (English)
[J] Eur. J. Oper. Res. 143, No. 2, 377-389 (2002). ISSN 0377-2217

Summary: In this paper sufficient regularity and coercivity conditions for Minty and Stampacchia type variational inequality systems are offered. The typical results state that if the independent inequalities are solvable, and the functions involved are lower semicontinuous, then the system has also a solution, that is, a factorization principle holds. As an application, a variational inequality system consisting of two partial differential inequalities is considered. This result is analogous to that of {\it Y.-Q. Chen} [J. Math. Anal. Appl. 231, No. 1, 177--192 (1999; Zbl 0934.47031)] obtained for a variational inequality.

MSC 2000:: *49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators
90C33 Complementarity problems

Keywords: variational inequality systems; Minty variational inequality; Stampacchia variational inequality; Kakutani fixed point theorem; partial differential inequality system

Citations: Zbl 0934.47031

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