Geodesic
Existence of viable solutions for nonconvex differential inclusions
Electronic Journal of Differential Equations, Tome 2005 (2005).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Bounkhel, Messaoud and Haddad, Tahar},
     title = {Existence of viable solutions for nonconvex differential inclusions},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2005},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a271/}
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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__a271/