On the Discontinuous Infinite-Dimensional Generalized Quasivariational Inequality Problem

Abstract

In this paper, we deal with the following generalized quasi-variational inequality problem: given a real normed space E with topological dual E* and two multifunctions G: X → 2x and F: X→2E*, find (x , φ ) ∈ X × E* such that x∈G(x), φ∈F(x), 〈φ, x-y〉 ≤ 0, for all y ∈ G(x). We extend to such infinite-dimensional setting some existence results which have been obtained recently for the special case where E is finite dimensional. In particular, our assumptions do not imply any kind of continuity for the multifunction F.