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2012 | 32 | 1 | 63-85
Tytuł artykułu

On functional differential inclusions in Hilbert spaces

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EN
Abstrakty
EN
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.
Twórcy
  • University Sultan My Slimane, Faculty polydisciplinary, BP 592, Mghila, Beni Mellal, Morocco
Bibliografia
  • [1] M. Aitalioubrahim and S. Sajid, viability problem with perturbation in Hilbert space, Electron. J. Qual. Theory Differ. Equ. 7 (2007) 1-14.
  • [2] J.P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, 1984. doi: 10.1007/978-3-642-69512-4
  • [3] M. Bounkhel, Existence results of nonconvex differential inclusions, Portugal. Math. 59 (3) (2002) 283-310.
  • [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] A. Cernea and V. Lupulescu, Viable solutions for a class of nonconvex functional differential inclusions, Math. Reports 7(57) (2) (2005) 91-103.
  • [6] F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley and Sons, 1983.
  • [7] F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory, Springer, New York, 1998.
  • [8] K. Deimling, Multivalued Defferential Equations. De Gruyter Series in Non linear Analysis and Applications, Walter de Gruyter, Berlin, New York, 1992.
  • [9] A. Gavioli and L. Malaguti, Viable solutions of differential inclusions with memory in Banach spaces, Portugal. Math. 57 Fasc. 2 (2000).
  • [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]G. Haddad, Monotone trajectories for functional differential inclusions, J. Differential Equations 42 (1981) 1-24. doi: 10.1016/0022-0396(81)90031-0
  • [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] A. Syam, Contributions aux Inclusions Différentielles, Ph. thesis, Université Montpellier II, 1993.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1139
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