The Behaviour of Solutions of Ordinary Differential Equations in Infinite Domains

  • Ya. I. Zhitomirskii
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 98)


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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  1. [1]
    Naimark, M. A.: Linear differential operators, New York, F. Ungar Pub. Co. 1967.zbMATHGoogle Scholar
  2. [2]
    Zolotaryov, G. N.: Uniqueness theorems for a class of integral representations, Matem. Sbornik, v.78(120), 1969, 408.Google Scholar
  3. [3]
    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.Google Scholar
  4. [4]
    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.Google Scholar
  5. [5]
    Zhitomirskii, Ya. I.: On the asymptotics of solutions of systems of linear equations in expanding domains, Diff. Uravn., V.XII, N 8, 1976, 1427.Google Scholar
  6. [6]
    Gel’fand, I. M. and Shilov, G. E.: Theory of differential equations Series title: Generalized functions, v. 3., New York, Academic Press, 1967, 307p.Google Scholar

Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  • Ya. I. Zhitomirskii
    • 1
  1. 1.HaifaIsrael

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