manuscripta mathematica

, Volume 31, Issue 1–3, pp 285–296 | Cite as

Eine Bemerkung zur lokalen Werteverteilung der Lösungen linearer Differentialgleichungen

  • Otto Knab
Article
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Abstract

We consider the homogeneous linear differential equation
$$w^{(n)} + \sum\limits_{j = 1}^n {f_{n - j} } (z)w^{(n - j)} = 0$$
(D)
with coefficients fn-j holomorphic in the disc |z-ζ|<R. If w is the solution of an initial value problem for (D) in z=ζ, then we construct a lower bound for the radius of disconjugacy of w, depending on the initial values and the first step of the central index of the Taylor's series of the fn-j about z=ζ.
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Literaturverzeichnis

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    HAYMAN, W. K.: Differential inequalities and local valency. Pacific J. Math.44, 117–137 (1973)Google Scholar
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    RAHMAN, Q. J., STANKIEWICZ, J.: Differential inequalities and local valency. Pacific J. Math.54, 165–181 (1974)Google Scholar
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    VOORHOEVE, M.: Zeros of exponential polynomials. Dissertation, Leiden 1977Google Scholar
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    VOORHOEVE, M., VAN DER POORTEN, A. J., TIJDEMAN, R.: On the number of zeros of certain functions. Nederl. Akad. Wet., Proc., Ser. A78=Indagationes math.37, 407–416 (1975)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Otto Knab
    • 1
  1. 1.Mathematisches Institut I der Universität KarlsruheKarlsruheBundesrepublik Deutschland

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