Existence of a solution to nonlinear variational inequality under generalized positive homogeneity

We establish several new existence theorems for nonlinear variational inequalities with generalized positively homogeneous functions. The results presented here are general enough to include two Mor e existence theorems of complementarity problems as the special cases. We also establish an existence result for the nonlinear complementarity problem with an exceptional regularity map. The concept of exceptional family for variational inequality plays a key role in our analysis.