Implicit dynamical systems and quasi variational inequalities

Abstract

In this paper, we propose and analyze some implicit projected dynamical systems associated with quasi variational inequalities by using the techniques of the projection and the Wiener–Hopf equations. We prove that the globally asymptotic stability of these dynamical systems requires only the pseudomonotonicity of the operator, which is a weaker condition than monotonicity. We also discuss some special cases, which can be obtained from our main results. The results obtained in this paper represent a significant improvement of the previously known results.