Abstract
We prove theorems on asymptotic, equiasymptotic, and uniform asymptotic stability of the integral sel of a nonautonomous system of ordinary differential equations.
Similar content being viewed by others
References
V. V. Rumyantsev and A. S. Oziraner,Stability and Stabilization of Motion with Respect to the Part of Variables [in Russian] Nauka, Moscow 1987.
A. Ya. Savchenko and A. O. Ignat’ev,Problems of Stability of Nonautonomous Dynamical Systems [in Russian] Naukova Dumka, Kiev 1989.
V. I. Zubov,Stability of Motion [in Russian] Vysshaya Shkola, Moscow 1973.
A. M. Samoilenko,Elements of the Mathematical Theory of Multifrequency Oscillations [in Russian] Nauka, Moscow 1987.
Yu. A. Mitropol’skii and O. B. Lykova,Integral Manifolds in Nonlinear Mechanics [in Russian] Nauka, Moscow 1973.
N. Rouche, P. Habets, and M. Laloy,Stability Theory by Liapunov’s Direct Method, Springer, Berlin 1977.
A. O. Ignat’ev, “Application of the Lyapunov method to the investigation of integral sets,”Ukr. Mat. Zh.,44, No. 10. 1342–1348 (1992).
A. O. Ignat’ev, “On the existence of Lyapunov functions in problems of stability of integral sets,”Ukr. Mat. Zh.,45, No. 7, 932–941 (1993).
V. M. Matrosov, “Stability of Motion,”Prikl. Mat. Mekh.,26, No. 5, 885–895 (1962).
Rights and permissions
About this article
Cite this article
Ignat’ev, A.O. Asymptotic stability of integral sets. Ukr Math J 48, 1202–1213 (1996). https://doi.org/10.1007/BF02383866
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02383866