Second-order viability result in Banach spaces

• Autorzy: Myelkebir Aitalioubrahim , Said Sajid
• Języki publikacji: 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.

Słowa kluczowe

EN

differential inclusion,viability; measurability; selection

Kategorie tematyczne

• 34A60: Differential inclusions

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2010
• Tom: 30
• Numer: 1
• Strony: 5-21

Daty

wydano

2010

otrzymano

2007-03-25

Twórcy

autor

Myelkebir Aitalioubrahim

• University Hassan II-Mohammedia, U.F.R Mathematics and Applications, F.S.T, BP 146, Mohammedia, Morocco

autor

Said Sajid

• University Hassan II-Mohammedia, U.F.R Mathematics and Applications, F.S.T, BP 146, Mohammedia, Morocco

Bibliografia

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• [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.

Identyfikatory

DOI

10.7151/dmdico.1109