Abstract
We investigate smoothness properties of the roots of algebraic equations with almost constant coefficients and construct a transformation, which may be efficiently used for the investigation of the asymptotic behavior of a fundamental family of solutions of a broad class of nonautonomous linear differential equations of the nth order.
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REFERENCES
I. T. Kiguradze and T. A. Chanturiya, Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations [in Russian], Nauka, Moscow (1990).
I. T. Kiguradze, “On asymptotic representation of solutions of linear differential equations,” Tr. Tbilisi Univ., 102, 149–167 (1964).
M. Matell, Asymptotic Eigenschaften Gewisser Linearer Differential-Gleichungen, Appelbergs Boktrycheri Actiobolag, Uppsala (1924).
N. Levinson, “The asymptotic nature of solutions of linear systems of differential equations,” Duke Math. J., 15, 111–126 (1948).
E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York (1955).
N. I. Shkil', “Asymptotic solution of a system of linear differential equations in the case of multiple roots of the characteristic equation,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., 2(39), 176–185 (1964).
A. Devinatz, “The asymptotic nature of the solutions of certain linear systems of differential equations,” Pacific. J. Math., 15, 75–83 (1965).
N. I. Shkil', “Reduction of systems of linear differential equations to the generalized L-diagonal form,” Differents. Uravn., 2, No. 11, 1436–1443 (1966).
M. I. Shkil', Asymptotic Methods in Differential Equations [in Ukrainian], Vyshcha Shkola, Kiev (1971).
A. Devinatz, “An asymptotic theorem for systems of linear differential equations,” Trans. Amer. Math. Soc., 160, 353–363 (1971).
A. Devinatz and J. I. Kaplan, “Asymptotic estimates for solutions of linear systems of ordinary differential equations having multiple characteristic roots,” Indiana Univ. Math. J., 22, No. 4, 355–366 (1972).
V. S. Privalov, Introduction to the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1977).
A. P. Mishina and I. V. Proskuryakov, Higher Algebra. Linear Algebra, Polynomials, and General Algebra [in Russian], Nauka, Kiev (1965).
A. I. Kostrikin, Introduction to Algebra [in Russian], Nauka, Moscow (1977).
V. M. Evtukhov, “Asymptotic integration of certain classes of linear differential equations,” Nelin. Kol., 3, No. 3, 334–357 (2000).
P. Hartman, Ordinary Differential Equations [Russian translation], Mir, Moscow (1970).
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Evtukhov, V.M. On Some Problems of the Asymptotic Theory of Linear Differential Equations of the nth Order. Ukrainian Mathematical Journal 54, 23–50 (2002). https://doi.org/10.1023/A:1019737418432
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DOI: https://doi.org/10.1023/A:1019737418432