Lyapunov functional-Razumikhin type theorems for stability of \(p\)-NFDE (Q1374828)

By introducing a distinction between unbounded and (asymptotically) infinite delays, as well as defining several auxiliary notions, an extension and apparent uniformization of a few theorems on \(V\)-functionals and their derivatives are obtained. The price paid is a stronger restriction of the notion of closeness of two functions in the already strongly restricted functional space. It is well-known (cf. Lyapunov's original papers) that stability depends crucially on the specific definition of ``closeness'' and that there are many non-equivalent definitions of this property. The examples provided are contrived and serve an illustrative purpose. Of interest only to abstractly minded persons.