Journal of Convex Analysis, Vol. 7, No. 1, pp. 183-195 (2000)

On the Second-Order Contingent Set and Differential Inclusions

Brahim Aghezzaf and Saïd Sajid

Département de mathématiques et d' informatique, Faculté des Sciences Aïn Chock, BP: 5366 Maarif, Casablanca, Maroc, and Département de mathématiques, F.S.T.M, BP. 146, Mohammadia, Maroc,

Abstract: In this paper, we establish the existence of solutions of a nonconvex second order differential inclusion of the following type:
\stackrel{..}{x}(t)\in F(x(t), \stackrel{.}{x}(t)) \text{ a.e, } x(0)=x_0\in K, \stackrel{.}{x}(0)=v_0\in \Omega,
such that $x(t)\in K$, where $K$ is a closed subset and $\Omega$ is an open subset of $\mathbb{R}^n$. When $K$ is in addition convex, we introduce the contingent cone $T_K$ to prove the existence of solutions of the differential inclusion:
\stackrel{..}{x}(t)\in G(x(t),\stackrel{.}{x}(t)) \text{ a.e, } x(t)\in K \text{ and } \stackrel{.}{x}(t)\in T_K(x(t))

Keywords: Continuous multifunctions, compact multifunctions, contingent cone, second-order contingent set

Classification (MSC2000): 34A60

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number]
© 2000 ELibM for the EMIS Electronic Edition