Skip to main content
SpringerLink
Log in

On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We prove that if an analytic function f with an isolated singular point at ∞ is a solution of the differential equation P(zlnz, f, f′) = 0, where P is a polynomial in all variables, then f has finite order. We study the asymptotic properties of a meromorphic solution with logarithmic singularity.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. V. V. Golubev, Lectures on Analytic Theory of Differential Equations [in Russian], Gostekhteorizdat, Moscow (1950).

    Google Scholar 

  2. G. Valiron, Fonctions Analytiques [Russian translation], Gostekhteorizdat, Moscow (1957).

    Google Scholar 

  3. A. I. Markushevich, Theory of Analytic Functions [in Russian], Vol. 2, Nauka, Moscow (1968).

    Google Scholar 

  4. A. A. Gol'dberg and I. V. Ostrovskii, Distribution of Values of Meromorphic Functions [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  5. A. Z. Mokhon'ko and V. D. Mokhon'ko, “On order of growth of analytic solutions for algebraic differential equations having logarithmic singularity,” Mat. Stud., 13, No. 2, 203–218 (2000).

    Google Scholar 

  6. A. A. Gol'dberg and A. Z. Mokhon'ko, “On the growth rate of solutions of algebraic differential equations in angular domains,” Differents. Uravn., 11, No. 9, 1568–1574 (1975).

    Google Scholar 

  7. A. Z. Mokhon'ko and V. D. Mokhon'ko, “Asymptotic estimates of growth of meromorphic solutions of differential equations in angular domains,” Sib. Mat. Zh., 41, No. 1, 185–199 (2000).

    Google Scholar 

  8. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  9. L. Schwartz, Analyse Mathématique [Russian translation], Vol. 1, Mir, Moscow (1972).

  10. Sh. I. Strelets, Asymptotic Properties of Analytic Solutions of Differential Equations [in Russian], Mintis, Vilnius (1972).

Download references

Author information

Authors and Affiliations

  1. “L'vivs'ka Politekhnika” National University, Lviv

    A. Z. Mokhon'ko & V. D. Mokhon'ko

Authors
  1. A. Z. Mokhon'ko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. D. Mokhon'ko
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mokhon'ko, A.Z., Mokhon'ko, V.D. On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point. Ukrainian Mathematical Journal 55, 1793–1809 (2003). https://doi.org/10.1023/B:UKMA.0000027043.58126.2e

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:UKMA.0000027043.58126.2e

Keywords

Search

Navigation