Electron. J. Diff. Eqns., Vol. 2005(2005), No. 114, pp. 1-11.

Caratheodory perturbation of a second-order differential inclusion with constraints

Saida Amine, Radouan Morchadi, Said Sajid

Abstract:
We prove the existence of local solutions for the second-order viability problem
$$ \ddot{x}(t) \in f(t,x(t),\dot{x}(t))+F(x(t),\dot{x}(t)),\quad x(t)\in K. $$
Here $K$ is a closed subset of $\mathbb{R}^{n}$, $F$ is an upper semicontinuous multifunction with compact values contained in the subdifferential of a convex proper lower semicontinuous function $V$, and $f$ is a Caratheodory function.

Submitted June 30, 2005. Published October 21, 2005.
Math Subject Classifications: 34A60.
Key Words: Upper semicontinuous multifunction; cyclically monotone; Caratheodory function.

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Saïda Amine
U.F.R Mathematics and Applications
Department of Mathematics
Faculty of Sciences and Techniques of Mohammedia
BP 146, Mohammedia, Morocco
email: aminesaida@hotmail.com
Radouan Morchadi
U.F.R Mathematics and Applications
Department of Mathematics
Faculty of Sciences and Techniques of Mohammedia
BP 146, Mohammedia, Morocco
email: morchadi@hotmail.com
Saïd Sajid
U.F.R Mathematics and Applications
Department of Mathematics
Faculty of Sciences and Techniques of Mohammedia
BP 146, Mohammedia, Morocco
email: saidsajid@hotmail.com

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