Geodesic
Existence of viable solutions for nonconvex differential inclusions
Electronic journal of differential equations, Tome 2005 (2005)
We show the existence result of viable solutions to the differential inclusion

$\displaylines{ \dot x(t)\in G(x(t))+F(t,x(t)) \cr x(t)\in S \quad \hbox{on } [0,T], }$

where $F: [0,T]\times H\to H(T>0)$ is a continuous set-valued mapping, $G:H\to H$ is a Hausdorff upper semi-continuous set-valued mapping such that $G(x)\subset \partial g(x)$, where $g :H\to \mathbb{R}$ is a regular and locally Lipschitz function and $S$ is a ball, compact subset in a separable Hilbert space $H$.
Classification : 34A60, 34G25, 49J52, 49J53
Keywords: uniformly regular functions, normal cone, nonconvex differential inclusions 
@article{EJDE_2005__2005__a171,
     author = {Bounkhel,  Messaoud and Haddad,  Tahar},
     title = {Existence of viable solutions for nonconvex differential inclusions},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1075.34053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a171/}
}
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Bounkhel,  Messaoud; Haddad,  Tahar. Existence of viable solutions for nonconvex differential inclusions. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a171/