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1996 | 16 | 1 | 53-74
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Existence and density results for retarded subdifferential evolution inclusions

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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].
  • University of Perugia, Department of Mathematics, Via Vanvitelli, 1 Perugia, 06123, Italy
  • University of Perugia, Department of Mathematics, Via Vanvitelli, 1 Perugia, 06123, Italy
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