On a class of implicit differential inclusions

Abstract

Existence of solutions is established for a class of implicit differential inclusions equivalent to explicit relations with nonconvex-valued, yet only upper semicontinuous right-hand side. Moreover, the set of stationary points is shown to be asymptotically stable if both of the set-valued maps involved are monotone and one of them is a subdifferential. Essentially, the primitive of the latter can be used as a natural Lyapunov function. © 1986.