Weak flow-invariance for non-convex differential inclusions
By using the Scorza Dragoni property the technique of directionally continuous selections [see \textit{A. Bressan}, Directionally continuous selections and differential inclusions, Funkc. Ekvacioj, Ser. Int. 31, No. 3, 459-470 (1988; Zbl 0676.34014)] is adapted to the Carathéodory lower semicontinuous, integrably bounded, closed valued multifunction \(F(t,x)\) and then, by the construction of polygonal approximations, the existence of a viable solution \(x(t)\in K\) for \(\dot x(t)\in F(T,x(t))\) is shown in the case when \(K\) is a locally compact subset of a reflexive Banach space and the function \(F\) satisfies the classical tangency condition: \(F(t,x)\) being contained in Bouligand's contingent cone \(T_ K(x)\).
scientific article; zbMATH DE number 90482