Geodesic
Existence of solutions for nonconvex second-order differential inclusions in the infinite dimensional space
Electronic journal of differential equations, Tome 2006 (2006)
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.
Classification : 34A60, 49J52
Keywords: nonconvex differential inclusions, uniformly regular functions 
@article{EJDE_2006__2006__a190,
     author = {Haddad,  Tahar and Yarou,  Mustapha},
     title = {Existence of solutions for nonconvex second-order differential inclusions in the infinite dimensional space},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1103.34055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a190/}
}
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Haddad,  Tahar; Yarou,  Mustapha. Existence of solutions for nonconvex second-order differential inclusions in the infinite dimensional space. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a190/