Discussiones Mathematicae Differential Inclusions 16(1) (1996) 53-74



Tiziana Cardinali and Simona Pieri

University of Perugia, Department of Mathematics
Via Vanvitelli, 1 Perugia, 06123, Italy


In this paper we study Cauchy problems for retarded evolution inclusions, where the Fréchet subdifferential of a function F:Ω→R∪{+∞} (Ω is an open subset of a real separable Hilbert space) having a φ-monotone subdifferential of oder two is present. First we establish the existence of extremal trajectories and we show that the set of these trajectories is dense in the solution set of the original convex problem for the norm topology of the Banach space C([-r, T0], Ω) ("strong relaxation theorem"). Then we prove that this density result allows one to establish a nonlinear "bang-bang principle" for a class of control systems with dealy on a nonconvex constraint. We want to observe that the results here extend those of [11] and [13].

Keywords: Fréchet subdifferential, subdifferential evolution inclusion, dealy, strong solution, extremal trajectory, solution set, relaxation theorem, bang-bang principle, control system.

1991 Mathematics Subject Classification: 34G20.


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