Abstract
We present new results on the exponential dichotomy on the entire axis of linear differential equations in \(\mathbb{R}^n\).
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REFERENCES
Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in a Banach Space [in Russian], Nauka, Moscow (1970).
A. D. Maizel', “On the stability of solutions of systems of differential equations,” Tr. Ural. Politekhn. Univ., Ser. Mat. 51, 20–50 (1954).
J. L. Massera and J. J. Schäffer, Linear Differential Equations and Function Spaces Academic Press, New York (1966).
V. L. Kulik, Dichotomy of Linear Differential Equations and Alternating Lyapunov Functions [in Russian], Doctoral-Degree Thesis (Physics and Mathematics), Kiev (1988).
V. A. Pliss, “Bounded solutions of inhomogeneous linear systems of differential equations,” in: Problems of the Asymptotic Theory of Nonlinear Oscillations [in Russian], Naukova Dumka, Kiev (1977), pp. 168–173.
Yu. A. Mitropol'skii, A. M. Samoilenko, and V. L. Kulik, Investigation of the Dichotomy of Linear Systems of Differential Equations Using the Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1990).
S. A. Chaplygin, A New Method for Approximate Integration of Differential Equations [in Russian], Fizmatgiz, Moscow-Leningrad (1950).
O. Perron, “Die Ordnungszahlen linear Differentialgleichungssysteme,” Math. Z. 31, 748–766 (1930).
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Samoilenko, A.M. On the Exponential Dichotomy on \(\mathbb{R}\) of Linear Differential Equations in \(\mathbb{R}^n\) . Ukrainian Mathematical Journal 53, 407–426 (2001). https://doi.org/10.1023/A:1012392221478
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DOI: https://doi.org/10.1023/A:1012392221478