Literature cited
E. A. Barbashin, “Construction of Lyapunov functions,” Differentsial'nye Uravneniya,4, No. 12 (1968).
N. G. Chetaev, Stability of Motion, Studies in Analytical Mechanics [in Russian], Izd. Akad. Nauk USSR, Moscow (1962).
A. A. Lebedev, “A method for constructing Lyapunov functions,” Prikl. Matem. i Mekh.,21, No. 1 (1957).
B. S. Razumikhin, “Stability of systems with a small parameter,” Prikl. Matem. i Mekh.,21, No. 4 (1957).
M. K. Yakovlev, “A method for constructing Lyapunov functions for linear systems with variable coefficients,” Differentsial'nye Uravneniya,1, No. 1 (1965).
M. O. Pustovoitov, “Constructing Lyapunov functions by the method of small parameter,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 10 (1969).
A. M. Lyapunov, General Problem of Stability of Motion [in Russian], Gostekhizdat, Moscow-Leningrad (1950).
N. V. Azbelev, I. M. Smolin, and Z. B. Tsalyuk, “An approximate method for constructing Cauchy functions,” Dokl. Akad. Nauk SSSR,135, No. 3 (1960).
A. A. Martynyuk, “An implementation of a rapidly convergent iteration process for solving differential equations and some applications,” Ukrainsk. Matem. Zh.,22, No. 6 (1970).
A. D. Gorbunov, “Some problems of the qualitative theory of ordinary linear homogeneous differential equations with variable coefficients,” Uch. Zap. MGU, Matematika,7, No. 165 (1959).
R. Bellman, Introduction to the Theory of Matrices [Russian translation], Nauka, Moscow (1969).
V. I. Zubov, Lyapunov Methods and Their Application [in Russian], Izd-vo LGU (1957).
A. A. Martinyuk, “Constructing integral matrices,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 1 (1971).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 2, No. 2, pp. 255–260, March–April, 1972.
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Martynyuk, A.A. An iteration formula for Lyapunov-function construction. Ukr Math J 24, 211–216 (1972). https://doi.org/10.1007/BF01086816
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DOI: https://doi.org/10.1007/BF01086816