Abstract
We develop the method of Lyapunov functionals in the stability analysis of linear nonautonomous functional-differential equations of neutral type. The approach is based on the construction of limit equations and limit Lyapunov functionals.
Similar content being viewed by others
References
J. K. Hale and J. Kato, “Phase space for retarded equations with infinite delay,”Funkcial. Ekvac.,21, No. 1, 11–41 (1978).
S. Murakami, “Perturbation theorems for functional-differential equations with infinite delay via limiting equations,”J. Differ. Equat.,59, 314–335 (1985).
A. A. Martynyuk, D. Kato, and A. A. Shestakov,Stability of Motion: The Method of Limit Equations [in Russian], Naukova Dumka, Kiev (1990).
A. S. Andreev and D. Kh. Khusanov, “The method of Lyapunov functionals in the asymptotic stability/instability problem,”Differentsial’nye Uravneniya [Differential Equations],34, No. 7, 876–885 (1998).
A. S. Andreev,Methods for Stability Analysis of Nonautonomous Equations [in Russian], Moskov. Gos. Univ., Ulyanovsk Branch, Ulyanovsk (1994).
V. B. Kolmanovskii and V. R. Nosov,Stability and Periodic Modes of Adaptable Systems with Aftereffect [in Russian] Nauka, Moscow (1981).
J. Hale,Theory of Functional Differential Equations, Springer-Verlag, New York-Heidelberg (1977).
Author information
Authors and Affiliations
Additional information
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 323–331, September, 2000.
Rights and permissions
About this article
Cite this article
Andreev, A.S., Pavlikov, S.V. The method of Lyapunov functionals in stability analysis of functional-differential equations. Math Notes 68, 281–288 (2000). https://doi.org/10.1007/BF02674550
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02674550