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.