A note on pseudomonotone functions, regularization, and relaxed coerciveness Original Research Article

This note continues earlier work on pseudomonotone functions and variational inequalities. First we show some invariance properties of this concept of pseudomonotonicity due to Brézis. Then we study variational inequalities with pseudomonotone functions on noncompact sets. We exhibit the relation between the existence of solutions in the noncoercive situation and the convergence of an abstract regularization procedure. Then we extend an existence theorem of the author under semicoerciveness assumptions and a more recent existence result due to Tomarelli under compactness — compatibility assumptions to the general setting of pseudomonotone functions.