Electron. J. Diff. Equ., Vol. 2012 (2012), No. 30, pp. 1-13.

Higher order viability problem in Banach spaces

Myelkebir Aitalioubrahim, Said Sajid

Abstract:
We show the existence of viable solutions to the differential inclusion
$$\displaylines{ x^{(k)}(t) \in F(t,x(t))\cr x(0)=x_{0},\quad x^{(i)}(0)=y^i_{0},\quad i=1,\dots,k-1,\cr x(t) \in K\quad\hbox{on } [0,T], }$$
where $k \geq 1$, K is a closed subset of a separable Banach space and F(t,x) is an integrable bounded multifunction with closed values, (strongly) measurable in t and Lipschitz continuous in x.

Submitted May 30, 2011. Published February 21, 2012.
Math Subject Classifications: 34A60.
Key Words: Differential inclusion; measurability; selection; viability.

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Myelkebir Aitalioubrahim
University Hassan II-Mohammedia
Laboratory Mathematics, Cryptography and Mecanics
F.S.T, BP 146, Mohammedia, Morocco
email: aitalifr@yahoo.fr
Said Sajid
University Hassan II-Mohammedia
Laboratory Mathematics, Cryptography and Mecanics
F.S.T, BP 146, Mohammedia, Morocco
email: saidsajid@hotmail.com

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