Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 114, pp. 1-11.
Title: Caratheodory perturbation of a second-order differential
inclusion with constraints
Authors: Saida Amine (Faculty of Sciences, Mohammedia, Morocco)
Radouan Morchadi (Faculty of Sciences, Mohammedia, Morocco)
Said Sajid (Faculty of Sciences, Mohammedia, Morocco)
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.