On the regularity of the boundary of the integral funnel of a differential inclusion
The paper deals with the differential inclusion \[ x'(t)\in F(t,x(t)),\;t\in [t_0,t_1]. \] The integral funnel of the above inclusion, issuing from a compact set \(K\subset \mathbb{R}^n\), is the set \[ \Omega(K)=\{(t,x(t)):t\in [t_0,t_1],\, x(\cdot) \text{ is a solution of the inclusion },\, x(t_0)\in K\}. \] Regularity theorems on the boundary of the integral funnel are established, under two distinct sets of assumptions on \(F\) and \(K\).
scientific article; zbMATH DE number 6668672
scientific article