Geodesic
On functional differential inclusions in Hilbert spaces
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 32 (2012) no. 1, pp. 63-85.

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We prove the existence of monotone solutions, of the functional differential inclusion ẋ(t) ∈ f(t,T(t)x) +F(T(t)x) in a Hilbert space, where f is a Carathéodory single-valued mapping and F is an upper semicontinuous set-valued mapping with compact values contained in the Clarke subdifferential ∂_c V(x) of a uniformly regular function V.
Keywords: functional differential inclusion, regularity, Clarke subdifferential 
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Aitalioubrahim, Myelkebir. On functional differential inclusions in Hilbert spaces. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 32 (2012) no. 1, pp. 63-85. http://geodesic.mathdoc.fr/item/DMDICO_2012_32_1_a2/

[1] [1] M. Aitalioubrahim and S. Sajid, viability problem with perturbation in Hilbert space, Electron. J. Qual. Theory Differ. Equ. 7 (2007) 1-14.

[2] [2] J.P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, 1984. doi: 10.1007/978-3-642-69512-4

[3] [3] M. Bounkhel, Existence results of nonconvex differential inclusions, Portugal. Math. 59 (3) (2002) 283-310.

[4] [4] A. Bressan, A. Cellina and G. Colombo, Upper semicontinuous differential inclusions without convexity, Proc. Amer. Math. Soc. 106 (1989) 771-775. doi: 10.1090/S0002-9939-1989-0969314-6

[5] [5] A. Cernea and V. Lupulescu, Viable solutions for a class of nonconvex functional differential inclusions, Math. Reports 7(57) (2) (2005) 91-103.

[6] [6] F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley and Sons, 1983.

[7] [7] F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory, Springer, New York, 1998.

[8] [8] K. Deimling, Multivalued Defferential Equations. De Gruyter Series in Non linear Analysis and Applications, Walter de Gruyter, Berlin, New York, 1992.

[9] [9] A. Gavioli and L. Malaguti, Viable solutions of differential inclusions with memory in Banach spaces, Portugal. Math. 57 Fasc. 2 (2000).

[10] [10] G. Haddad, Monotone trajectories of differential inclusions and functional differential inclusions with memory, Israel J. Math. 39 (1981) 83-100. doi: 10.1007/BF02762855

[11] [11]G. Haddad, Monotone trajectories for functional differential inclusions, J. Differential Equations 42 (1981) 1-24. doi: 10.1016/0022-0396(81)90031-0

[12] [12] R.T. Rockafellar, Generalized directional derivatives and subgradients of nonconvex functions, Canad. J. Math. 39 (1980) 257-280. doi: 10.4153/CJM-1980-020-7

[13] [13] A. Syam, Contributions aux Inclusions Différentielles, Ph. thesis, Université Montpellier II, 1993.