Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 173, pp. 1-8.
Title: Application of Pettis integration to differential inclusions
with three-point boundary conditions in Banach spaces
Authors: Dalila Azzam-Laouir (Univ. de Jijel, Algerie)
Imen Boutana (Univ. de Jijel, Algerie)
Abstract:
This paper provide some applications of Pettis integration to differential
inclusions in Banach spaces with three point boundary conditions of the form
$$
\ddot{u}(t) \in F(t,u(t),\dot u(t))+H(t,u(t),\dot u(t)),\quad
\hbox{a.e. } t \in [0,1],
$$
where $F$ is a convex valued multifunction upper semicontinuous on
$E\times E$ and $H$ is a lower semicontinuous multifunction.
The existence of solutions is obtained under the non convexity condition
for the multifunction $H$, and the assumption that
$F(t,x,y)\subset \Gamma_{1}(t)$,
$H(t,x,y)\subset \Gamma_{2}(t)$, where the multifunctions
$\Gamma_{1},\Gamma_{2}:[0,1]\rightrightarrows E$ are uniformly Pettis
integrable.
Submitted September 5, 2007. Published December 06, 2007.
Math Subject Classifications: 34A60, 28A25, 28C20.
Key Words: Differential inclusions; Pettis-integration; selections.