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On the sequences of zeros of holomorphic solutions of linear second-order differential equations

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Abstract

We find necessary and sufficient conditions under which a finite or infinite sequence of complex numbers is the sequence of zeros of a holomorphic solution of the linear differential equation f″ + a 0 f = 0 with a meromorphic coefficient a 0 that has second-order poles. In addition, we present a criterion for all solutions of second-order linear equations to be meromorphic.

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Authors and Affiliations

  1. Drogobych State Pedagogical University, Drogobych, Ukraine

    B. V. Vinnitskii & E. V. Shavala

Authors
  1. B. V. Vinnitskii
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  2. E. V. Shavala
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Original Russian Text © B.V. Vinnitskii, E.V. Shavala, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 10, pp. 1306–1310.

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Vinnitskii, B.V., Shavala, E.V. On the sequences of zeros of holomorphic solutions of linear second-order differential equations. Diff Equat 44, 1361–1366 (2008). https://doi.org/10.1134/S0012266108100029

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  • DOI: https://doi.org/10.1134/S0012266108100029

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