On the existence of Lyapunov functions in problems of stability of integral sets
A nonautonomous system of ordinary differential equations is considered. If this system admits a uniformly asymptotically stable integral set, then a neighborhood of this set contains a function similar to the Lyapunov function.
English version (Springer): Ukrainian Mathematical Journal 45 (1993), no. 7, pp 1031-1041.
Citation Example: Ignat'ev A. O. On the existence of Lyapunov functions in problems of stability of integral sets // Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 932–941.