Vibrocorrect differential equations with measures (Q1086720)

Let \(AC_ m\) denote the space of m-dimensional absolutely continuous functions. The author shows that if the function F(x,u,\D{u},t), with \(U\in AC_ m\), is linear in \D{u}, continuous in all its variables and satisfies the Lipschitz condition in x, then a unique solution \(x(t)=V[u(t)]\) of the differential equation, \(\dot x=F(x,u(t),u(t),t),\) \(x(t_ 0)=x_ 0\) exists for all \(t\geq t_ 0\).