Abstract
Under minimal restrictions on coefficients of linear ODEs with linear complex parameter λ we find asymptotics of solutions x(t, λ) as |λ| → ∞ and |t|≤ q(|λ|), where q(|λ|) is an increasing function determined by coefficients, and obtain an estimate of solutions for all (t, λ) ∈ ℝ × ℂ.
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References
Naimark, M. A.: Linear differential operators, New York, F. Ungar Pub. Co. 1967.
Zolotaryov, G. N.: Uniqueness theorems for a class of integral representations, Matem. Sbornik, v.78(120), 1969, 408.
Zhitomirskii, Ya. L: Uniqueness classes for solutions of the Cauchy problem, Dokl. Akad. Nauk SSSR V. 172, 1967, No.6= Soviet Math. Dokl. Vol.8, 1967, No.1, 259.
Zhitomirskii, Ya. L: Uniqueness classes for the solution of the Cauchy problem for linear equations with rapidly growing coefficients, Dokl. Akad. Nauk SSSR, V. 173, 1967, No. 1= Soviet Math. Dokl. Vol. 8,1967, No.2, 317.
Zhitomirskii, Ya. I.: On the asymptotics of solutions of systems of linear equations in expanding domains, Diff. Uravn., V.XII, N 8, 1976, 1427.
Gel’fand, I. M. and Shilov, G. E.: Theory of differential equations Series title: Generalized functions, v. 3., New York, Academic Press, 1967, 307p.
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Zhitomirskii, Y.I. (1997). The Behaviour of Solutions of Ordinary Differential Equations in Infinite Domains. In: Gohberg, I., Lyubich, Y. (eds) New Results in Operator Theory and Its Applications. Operator Theory: Advances and Applications, vol 98. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8910-0_19
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DOI: https://doi.org/10.1007/978-3-0348-8910-0_19
Publisher Name: Birkhäuser, Basel
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