Electron. J. Diff. Eqns., Vol. 2006(2006), No. 33, pp. 1-8.

Existence of solutions for nonconvex second-order differential inclusions in the infinite dimensional space

Tahar Haddad, Mustapha Yarou

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 Caratheodory 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.

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Tahar Haddad
Department of Mathematics
Faculty of Sciences, Jijel University, Algeria
email: haddadtr2000@yahoo.fr
Mustapha Yarou
Department of Mathematics
Faculty of Sciences, Jijel University, Algeria
email: mfyarou@yahoo.com

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