Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 33, pp. 1-8.
Title: Existence of solutions for nonconvex second-order
differential inclusions in the infinite dimensional space
Authors: Tahar Haddad (Jijel Univ., Algeria)
Mustapha Yarou (Jijel Univ., Algeria)
Abstract:
We prove the existence of solutions to the differential
inclusion
$$
\ddot{x}(t)\in F(x(t),\dot{x}(t))+f(t,x(t),\dot{x}(t)), \quad
x(0)=x_{0}, \quad \dot{x}(0)=y_{0},
$$
where $f$ is a Carath\'{e}odory function and $F$
with nonconvex values in a Hilbert space such that
$F(x,y)\subset \gamma (\partial g(y))$, with $g$ a regular
locally Lipschitz function and $\gamma $ a linear operator.
Submitted December 12, 2005. Published March 16, 2006.
Math Subject Classifications: 34A60, 49J52.
Key Words: Nonconvex differential inclusions; uniformly regular functions.