Existence of generalized variational inequalities

This paper investigates certain generalized variational inequalities in Hilbert spaces which contain general mildly nonlinear variational inequalities and the classical variational inequalities as special cases. It employs the fixed point technique used by Glowinski, Lions and Stampacchia to obtain some existence results for these nonlinear inequalities. In particular, some existence results are obtained for both general mildly nonlinear variational inequalities and implicit complementarity problems.