Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 30, pp. 1-13.

Title: Higher order viability problem in Banach spaces

Authors: Myelkebir Aitalioubrahim (Univ. Hassan II-Mohammedia, Morocco)
         Said Sajid   (Univ. Hassan II-Mohammedia, Morocco)

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.