Skip to main content
Log in

A Further Note on a Result of Bank, Frank, and Laine

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we generalize a result of Bank, Frank, and Laine [2] and a result of Wang [8]. Under certain conditions on the coefficients Pj in equation (1.1), we show that solutions ƒ of (1.1) must satisfy λ(ƒ) = ρ(ƒ) or ƒ has only finitely many zeros.

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. S. Bank and G. Frank, A note on the distribution of zeros of solutions of linear differential equations, Comment Math. Univ. St. Paul. 33 (1984), 143–151.

    MathSciNet  MATH  Google Scholar 

  2. S. Bank, G. Frank, and I. Laine,:Uber die Nullstellen von Lösungen linearer Differentialgleichungen, Math. Z. 183 (1983), 355–364.

    Article  MathSciNet  MATH  Google Scholar 

  3. G. Gundersen, E. Steinbart and S. Wang, The possible orders of solutions of linear differential equations with polynomial coefficients, Trans. Amer. Math. Soc. 350 (1998), 1225–1247.

    Article  MathSciNet  MATH  Google Scholar 

  4. W. K. Hayman, Meromorphic Functions, Clarenden Press, Oxford, 1964.

    MATH  Google Scholar 

  5. I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin-New York, 1993.

    Book  Google Scholar 

  6. K. Pöschl, Über Anwachsen and Nullstellenverteilung der ganzen transzendenten Lösungen linearer Differentialgleichung, I, J. reine angew. Math. 199 (1958), 121–138.

    MathSciNet  MATH  Google Scholar 

  7. S. Wang, On the frequency of zeros of a fundamental solution set of complex linear differential equations, Kodai Math. J. 20 (1997), 143–155.

    Article  MathSciNet  MATH  Google Scholar 

  8. S. Wang, A note on a result of Bank, Prank and Laine, Complex Analysis and Differential Equations (Uppsala, 1997), 334–343, Acta Univ. Upsaliensis Skr. Uppsala Univ. C Organ. Hist., 64, Uppsala Univ., Uppsala, 1999.

  9. H. Wittich, Neuere Untersuchungen über eindeutige analytische Funktionen, 2nd Edition, Springer-Verlag, Berlin-Heidelberg-New York, 1968.

    Book  MATH  Google Scholar 

  10. H. Wittich, Über das Anwachsen der Lösungen linear Differentialgleichungen, Math. Ann. 124 (1952) 277–288.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Enid M. Steinbart.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Steinbart, E.M. A Further Note on a Result of Bank, Frank, and Laine. Results. Math. 42, 365–383 (2002). https://doi.org/10.1007/BF03322862

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03322862

1991 Mathematics subject classification

Key words

Navigation