Literature Cited
A. M. Lyapunov (M. A. Liapounoff), Probleme Général de Stabilité du Mouvement, Princeton University Press (1947).
B. P. Demidovich, “A generalization of the Lyapunov stability criterion for regular systems,” Mat. Sb.,66(108), No. 3, 344–353 (1965).
B. F. Bylov, R. É. Vinograd, D. M. Grobman, and V. V. Nemytskii, The Theory of Lyapunov Exponents and Its Applications to Problems of Stability [in Russian], Nauka, Moscow (1966).
N. Levinson, “The asymptotic behavior of a system of linear differential equations,” Am. J. Math.,68, 1–6 (1946).
E. V. Voskresenskii, “Componentwise asymptotics and homeomorphism of differential equations on manifolds,” Czechoslovak Math. J.,35, No. 3, 455–466 (1985).
F. Brauer, “Asymptotic equivalence and asymptotic behavior of linear systems,” Michigan Math. J.,9, 33–43 (1962).
N. Rouche, P. Habets, and M. Laloy, Stability Theory by Liapunov's Direct Method, Springer, New York (1977).
M. Rab, “Asymptotic relationships between the solutions of two systems of differential equations,” Ann. Polon. Math.,30, 119–124 (1974).
A. C. Lima, “A note on the asymptotic equivalence of two systems of differential equations,” Acta Fac. Rerum Natur. Univ. Comenian Math.,33(1977), 35–49 (1978).
Additional information
Saransk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 5, pp. 3–11, September–October, 1991.
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Voskresenskii, E.V. The comparison method in nonlinear analysis. Sib Math J 32, 725–733 (1991). https://doi.org/10.1007/BF00971171
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DOI: https://doi.org/10.1007/BF00971171