Skip to main content
Log in

Asymptotic solutions of a system of differential equations with multiple turning point

  • Published:
Ukrainian Mathematical Journal Aims and scope

Using a transformation matrix, we asymptotically reduce a system of differential equations with a small parameter in the coefficients of a part of derivatives and with multiple turning point to an integrable system of equations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. W. Wasow, Linear Turning Point Theory, Springer, New York (1985).

    MATH  Google Scholar 

  2. R. Y. Lee, “On uniform simplification of linear differential equation in a full neighborhood of a turning point,” J. Math. Anal. Appl., 27, 501–510 (1969).

    Article  MATH  MathSciNet  Google Scholar 

  3. R. J. Hanson, “Reduction theorems for systems of ordinary differential equations with a turning point,” J. Math. Anal. Appl., 16, 280–301 (1966).

    Article  MATH  MathSciNet  Google Scholar 

  4. R. J. Hanson and D. L. Russell, “Classification and reduction of second order systems at a turning point,” J. Math. Phys., 46, 74–92 (1967).

    MATH  MathSciNet  Google Scholar 

  5. Y. Sibuya, “Uniform simplification in a full neighborhood of a transition point,” Mem. Amer. Math. Soc., 149, 3–106 (1974).

    MathSciNet  Google Scholar 

  6. M. Kohno, S. Ohkohchi, and T. Kohmoto, “On full uniform simplification of even order linear differential equations with a parameter,” Hiroshima Math. J., 9, 747–767 (1979).

    MATH  MathSciNet  Google Scholar 

  7. T. Nishimoto, “On an extension theorem and its application for turning point problems of large order,” Kodai Math. Semin. Rep., 25, 458–489 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  8. H. L. Turritin, “Stokes multipliers for asymptotic solutions of a central differential equation,” Trans. Amer. Math. Soc., 68, 304–329 (1950).

    Article  MathSciNet  Google Scholar 

  9. A. M. Samoilenko, “On the asymptotic integration of a system of linear differential equations with a small parameter in the coefficients of a part of derivatives,” Ukr. Mat. Zh., 54, No. 11, 1505–1516 (2002).

    Google Scholar 

  10. A. M. Samoilenko and I. H. Klyuchnyk, “On the asymptotic integration of a linear system of differential equations with a small parameter in the coefficients of some derivatives,” Nelin. Kolyvannya, 12, No. 2, 208–234 (2009).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 11, pp. 1516–1530, November, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Klyuchnyk, I.H. Asymptotic solutions of a system of differential equations with multiple turning point. Ukr Math J 61, 1780–1797 (2009). https://doi.org/10.1007/s11253-010-0312-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-010-0312-z

Keywords

Navigation