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Asymptotics of a solution to a second order linear differential equation with large summands

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Abstract

We consider the second order ordinary differential equations whose coefficients of the unknowns contain smooth and rapidly oscillating summands proportional to the positive powers of the oscillation frequency. The complete asymptotic expansions are constructed and justified of solutions to the Cauchy problem.

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References

  1. Levenshtam V. B., “Asymptotic integration of differential equations with large high-frequency summands,“ Dokl. Akad. Nauk, 405, No. 2, 169–172 (2005).

    MathSciNet  Google Scholar 

  2. Levenshtam V. B., “Asymptotic integration of differential equations with rapidly oscillating terms of large amplitude. I,“ Differential Equations, 41, No. 6, 796–807 (2005).

    Article  MathSciNet  Google Scholar 

  3. Levenshtam V. B., “Asymptotic integration of differential equations with rapidly oscillating terms of large amplitude. II,“ Differential Equations, 41, No. 8, 1137–1145 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  4. Levenshtam V. B. and Khatlamadshiyan G. L., “Extension of averaging theory to differential equations containing rapidly oscillating terms with large amplitude. The problem of periodic solutions,“ Russian Math. (Iz. VUZ), 50, No. 6, 33–45 (2006).

    MATH  MathSciNet  Google Scholar 

  5. Moiseev N. N., Asymptotic Methods in Nonlinear Mechanics [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  6. Daletskiĭ Yu. L., “Asymptotic methods for some differential equations with oscillating coefficients,“ Dokl. Akad. Nauk SSSR, 143, No. 5, 1027–1029 (1962).

    Google Scholar 

  7. Daletskiĭ Yu. L. and Kreĭn M. G., Stability of Solutions to Differential Equations in Banach Space [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  8. Nayfeh A., Introduction to Perturbation Techniques [Russian translation], Mir, Moscow (1984).

    Google Scholar 

  9. Krasnosel’skiĭ M. A., The Shift Operator on the Trajectories of Differential Equations [in Russian], Nauka, Moscow (1966).

    Google Scholar 

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Authors and Affiliations

  1. Southern Federal University, Rostov-on-Don, Russia

    E. V. Krutenko & V. B. Levenshtam

Authors
  1. E. V. Krutenko
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  2. V. B. Levenshtam
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Correspondence to E. V. Krutenko.

Additional information

Original Russian Text Copyright © 2010 Krutenko E. V. and Levenshtam V. B.

The second author was supported in part by the Southern Mathematical Institute of the Vladikavkaz Scientific Center.

Rostov-on-Don. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 1, pp. 74–89, January–February, 2010.

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Krutenko, E.V., Levenshtam, V.B. Asymptotics of a solution to a second order linear differential equation with large summands. Sib Math J 51, 57–71 (2010). https://doi.org/10.1007/s11202-010-0008-5

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  • DOI: https://doi.org/10.1007/s11202-010-0008-5

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