The essential components of the set of equilibrium points for set-valued maps

In this article, we discuss the stability of equilibrium points for set-valued maps. We introduce the notion of essential components of the set of equilibrium points for set-valued maps and prove an existence theorem of essential components. As applications, we deduce the existence of essential components of the set of coincidence points and show that every Marchaud dynamical economy (cf. [J.P. Aubin, Dynamic Economic Theory, Springer-Verlag, 1997]) possesses at least one essential component of the set of its viable equilibrium points. (C) 2004 Elsevier Inc. All rights reserved.