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Second-order differential inclusions with Lipschitz right-hand sides

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Author(s): Dalila Azzam-Laouir | Fatiha Bounama

Journal: Electronic Journal of Differential Equations
ISSN 1072-6691

Volume: 2010;
Issue: 85,;
Start page: 1;
Date: 2010;
Original page

Keywords: Differential inclusion | Lipschitz multifunction

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