Existence and Relaxation Theorems for Unbounded Difierential Inclusions
A. Iofie · 2006
ẋ ∈ F (t, x) (1) on the given time interval, say [0, 1]. Here F is a set-valued mapping from [0, 1]×Rn into R (we shall write F : [0, 1]×Rn ⇒ Rn in what follows) with closed values which will be assumed nonempty whenever necessary. The classical theorems of Filippov and Wazewski use, as the main assumption characterizing the dependence of F on x, the standard Lipschitz condition h(F (t, x), F (t, x′)) ≤ k(t)‖x− x′‖,