On the asymptotic behavior of the solutions of nonstationary pseudolinear systems

Authors

  • A.A. Martynyuk
  • L.N. Chernetskaya

DOI:

https://doi.org/10.15407/dopovidi2014.12.064

Keywords:

pseudolinear systems of equations, stability via integral inequalities

Abstract

We consider a class of pseudolinear systems of equations of perturbed motion. The sufficient conditions of boundedness and stability via integral inequalities are derived. As an example, we considered a linear system of equations with almost constant coefficients.

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References

Bellman R. The theory of the stability of solutions of differential equations, Moscow: Izd-vo inostr. lit-ry, 1954 (in Russian).

Rama Mohana Rao M. Ordinary differential equations. theory and applications, New Delhi-Madras: Affiliated East-West Press, 1980.

Martynyuk A. A., Lakshmikantam V., Lila S. Resistance movements: the method of integral inequalities, Kiev: Nauk. Dumka, 1989 (in Russian).

Lyapunov A. M. The general problem of stability of motion, Leningrad; Moscow: ONTI, 1935 (in Russian).

Tonkov E. L. Stability of solutions of ordinary differential equations, Moscow: Mosc. in-t khim. mashynostroeniia, 1972 (in Russian).

Bylov B. F., Vinograd R. E. et al. The theory of Lyapunov exponents and its application to stability issues, Moscow: Nauka, 1966 (in Russian).

Hoppensteadt F. C. Analysis and simulation of chaotic systems, Berlin: Springer, 1993. https://doi.org/10.1007/978-1-4757-2275-8

Published

19.03.2025

How to Cite

Martynyuk, A., & Chernetskaya, L. (2025). On the asymptotic behavior of the solutions of nonstationary pseudolinear systems . Reports of the National Academy of Sciences of Ukraine, (12), 64–70. https://doi.org/10.15407/dopovidi2014.12.064

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