On Asymptotic Behaviour of Solutions to Linear Differential Systems with Variable Coefficients via Characteristic Numbers

MR2761088 Haruhisa ISHIDA and Hyung-Ju LEE Haruhisa ISHIDA and Hyung-Ju LEE On Asymptotic Behaviour of Solutions to Linear Differential Systems with Variable Coefficients via Characteristic Numbers Funkcialaj Ekvacioj. Serio Internacia 53 2010 359--379 http://fe.math.kobe-u.ac.jp/FE/FullPapers/53-3/53_359.pdf http://www.ams.org/mathscinet-getitem?mr=MR2761088 We treat the system of linear differential equations with variable coefficients and examine its asymptotic behaviour via several characteristic numbers. Especially, we give a few conditions to admit the solution with polynomial order in terms of second exponent. Moreover, we establish an estimate of the solution to linear nonhomogeneous system by an inequality of Wazewski type, which leads to one of the Lyapunov exponent as well. Lozinski logarithmic norm, Lyapunov exponent, Nonhomogeneous linear differential equations, Wazewski's inequality. 34A30, 34D08. 53-359 2010 On Asymptotic Behaviour of Solutions to Linear Differential Systems with Variable Coefficients via Characteristic Numbers Haruhisa ISHIDA and Hyung-Ju LEE Haruhisa ISHIDA and Hyung-Ju LEE 1 Adrianova, L. Ya. Introduction to Linear Systems of Differential Equations Trans. Math. Monographs, 146, American Mathematical Society, Providence, RI 1995 MR1351004

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