Electron. J. Diff. Eqns., Vol. 2007(2007), No. 173, pp. 1-8.

Application of Pettis integration to differential inclusions with three-point boundary conditions in Banach spaces

Dalila Azzam-Laouir, Imen Boutana

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 6, 2007.
Math Subject Classifications: 34A60, 28A25, 28C20.
Key Words: Differential inclusions; Pettis-integration; selections.

An addendum was posted on September 15, 2016. It states a correction needed in Proposition 3.3. See the last page of this article.

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Dalila Azzam-Laouir
Laboratoire de Mathématiques Pures et Appliquées
Université de Jijel, Algérie
email: azzam_d@yahoo.com
Imen Boutana
Laboratoire de Mathématiques Pures et Appliquées
Université de Jijel, Algérie
email: bou.imend@yahoo.fr

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