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Periodic solutions of evolution problem associated with moving convex sets

Charles CastaingManuel D.P. Monteiro Marques — 1995

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper is concerned with periodic solutions for perturbations of the sweeping process introduced by J.J. Moreau in 1971. The perturbed equation has the form - D u N C ( t ) ( u ( t ) ) + f ( t , u ( t ) ) where C is a T-periodic multifunction from [0,T] into the set of nonempty convex weakly compact subsets of a separable Hilbert space H, N C ( t ) ( u ( t ) ) is the normal cone of C(t) at u(t), f:[0,T] × H∪H is a Carathéodory function and Du is the differential measure of the periodic BV solution u. Several existence results of periodic solutions for this...

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