Existence of generalized variational inequalities. (English) Zbl 0874.49012

Summary: We investigate certain generalized variational inequalities in Hilbert spaces which contain general mildly nonlinear variational inequalities and the classical variational inequalities as special cases. We employ the fixed point technique used by Glowinski, Lions and Stampacchia to obtain some existence results for these nonlinear inequalities. In particular, we obtain some existence results for both general mildly nonlinear variational inequalities and implicit complementarity problems.


49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
47J20 Variational and other types of inequalities involving nonlinear operators (general)
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
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