Existence Theorem for the Discontinuous Generalized Quasivariational Inequality Problem

We consider the following generalized quasivariational inequality problem: given a real Banach space E with topological dual E* and given two multifunctions G:X2 ^X and F:X2 ^E *, find such thatWe prove an existence theorem where F is not assumed to have any continuity or monotonicity property. Making use of a different technical construction, our result improves some aspects of a recent existence result (Theorem 3.1 of Ref. 1). In particular, the coercivity assumption of this latter result is weakened meaningfully.