Advertisement

Ukrainian Mathematical Journal

, Volume 56, Issue 4, pp 577–585 | Cite as

Malmquist theorem for solutions of differential equations in a neighborhood of a logarithmic singular point

  • A. A. Mokhon’ko
Article
  • 19 Downloads

Abstract

The Malmquist theorem (1913) on the growth of meromorphic solutions of the differential equation f ′ = P(z,f) / Q(z,f), where P(z,f) and Q(z,f) are polynomials in all variables, is proved for the case of meromorphic solutions with logarithmic singularity at infinity.

Keywords

Differential Equation Singular Point Logarithmic Singularity Meromorphic Solution Malmquist Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    Golubev, V. V. 1950Lectures on Analytic Theory of Differential EquationsGostekhteorizdatMoscow-Leningradin RussianGoogle Scholar
  2. 2.
    Malmquist, J. 1913Sur les fonctions á un nombre fini de branches définies par les équations différentielles du premier ordreActa Math.36297343Google Scholar
  3. 3.
    Gol’dberg, A. A., Levin, B. Y., Ostrovskii, I. V. 1991Entire and meromorphic functionsVINITI Series in Contemporary Problems in Mathematics (Fundamental Trends)VINITIMoscow5186in RussianGoogle Scholar
  4. 4.
    Gol’dberg, A. A., Ostrovskii, I. V. 1970Distribution of Values of Meromorphic FunctionsNaukaMoscowin RussianGoogle Scholar
  5. 5.
    Yosida, K. 1933A generalization of a Malmquist’s theoremJpn. J. Math.9239256Google Scholar
  6. 6.
    Markushevich, A. I. 1968Theory of Analytic FunctionsNaukaMoscowin RussianGoogle Scholar
  7. 7.
    Mokhon’ko, A. Z. 1981A field of algebroidal functions and estimates of their Nevanlinna characteristicsSib. Mat. Zh.22214218Google Scholar
  8. 8.
    A. Z. Mokhon’ko, “On Nevanlinna characteristics of some meromorphic functions,” Teor.Funkts.Funkts.Anal.Prilozhen., Issue 14, 83–87 (1971).Google Scholar
  9. 9.
    Mokhon’ko, A. Z., Mokhon’ko, V. D. 2000On order of growth of analytic solutions for algebraic differential equations having logarithmic singularityMat. Stud.13203218Google Scholar
  10. 10.
    Gold’berg, A. A., Mokhon’ko, A. Z. 1975On the growth rate of solutions of algebraic differential equations in angular domainsDifferents. Uravn.1115681574Google Scholar
  11. 11.
    Gol’dberg, A. A. 1975Nevanlinna lemma on the logarithmic derivative of a meromorphic functionMat. Zametki17525529Google Scholar
  12. 12.
    Mokhon’ko, A. Z. 1992On meromorphic solutions of algebraic differential equations in angular domainsUkr. Mat. Zh.44514523Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • A. A. Mokhon’ko
    • 1
  1. 1.Shevchenko Kiev National UniversityKiev

Personalised recommendations