Electron. J. Diff. Equ., Vol. 2010(2010), No. 85, pp. 1-9.

Second-order differential inclusions with Lipschitz right-hand sides

Dalila Azzam-Laouir, Fatiha Bounama

Abstract:
We study the existence of solutions of a three-point boundary-value problem for a second-order differential inclusion,
$$\displaylines{ \ddot u(t)\in F(t,u(t),\dot u(t)),\quad\hbox{a.e. }t\in [0,1],\cr u(0)=0, \quad u(\theta)=u(1). }$$
Here F is a set-valued mapping from $[0,1]\times E\times E$ to E with nonempty closed values satisfying a standard Lipschitz condition, and E is a separable Banach space.

Submitted March 29, 2010. Published June 18, 2010.
Math Subject Classifications: 34A60, 34B15, 47H10.
Key Words: Differential inclusion; Lipschitz multifunction

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Dalila Azzam-Laouir
Laboratoire de Mathématiques Pures et Appliquées
Département de Mathématiques
Université de Jijel, Algérie
email: laouir.dalila@gmail.com
Fatiha Bounama
Laboratoire de Mathématiques Pures et Appliquées
Département de Mathématiques
Université de Jijel, Algérie
email: bounamaf@yahoo.fr

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