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2010 | 30 | 1 | 5-21
Tytuł artykułu

Second-order viability result in Banach spaces

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EN
Abstrakty
EN
We show the existence result of viable solutions to the second-order differential inclusion
ẍ(t) ∈ F(t,x(t),ẋ(t)),
x(0) = x₀, ẋ(0) = y₀, x(t) ∈ K on [0,T],
where K is a closed subset of a separable Banach space E and F(·,·,·) is a closed multifunction, integrably bounded, measurable with respect to the first argument and Lipschitz continuous with respect to the third argument.
Twórcy
  • University Hassan II-Mohammedia, U.F.R Mathematics and Applications, F.S.T, BP 146, Mohammedia, Morocco
autor
  • University Hassan II-Mohammedia, U.F.R Mathematics and Applications, F.S.T, BP 146, Mohammedia, Morocco
Bibliografia
  • [1] B. Aghezzaf and S. Sajid, On the second-order contingent set and differential inclusions, J. Conv. Anal. 7 (1) (2000), 183-195.
  • [2] K.S. Alkulaibi and A.G. Ibrahim, On existence of monotone solutions for second-order non-convex differential inclusions in infinite dimensional spaces, Portugaliae Mathematica 61 (2) (2004), 231-143.
  • [3] S. Amine, R. Morchadi and S. Sajid, Carathéodory perturbation of a second-order differential inclusions with constraints, Electronic J. Diff. Eq. (2005), 1-11.
  • [4] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580, Springer-Verlag, Berlin-Heidelberg-New York, 1977. doi:10.1007/BFb0087685
  • [5] B. Cornet and G. Haddad, Théorème de viabilité pour les inclusions différentielles du seconde ordre, Isr. J. Math. 57 (2) (1987), 225-238.
  • [6] A. Dubovitskij and A.A. Miljutin, Extremums problems with constraints, Soviet Math. 4 (1963), 452-455.
  • [7] T.X. Duc Ha, Existence of viable solutions for nonconvex-valued differential inclusions in Banach spaces, Portugaliae Mathematica 52 Fasc. 2, 1995.
  • [8] M. Larrieu, Invariance d'un fermé pour un champ de vecteurs de Carathéodory, Pub. Math. de Pau, 1981.
  • [9] V. Lupulescu, A viability result for second order differential inclusions, Electron J. Diff. Eq. 76 (2003), 1-12.
  • [10] V. Lupulescu, Existence of solutions for nonconvex second order differential inclusions, Applied Math. E-notes 3 (2003), 115-123.
  • [11] R. Morchadi and S. Sajid, Noncovex second-order differential inclusion, Bulletin of the Polish Academy of Sciences 47 (3) (1999).
  • [12] Q. Zhu, On the solution set of differential inclusions in Banach spaces, J. Differ. Eq. 41 (2001), 1-8.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1109
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