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On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point

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Ukrainian Mathematical Journal Aims and scope

Assume that the coefficients and solutions of the equation f (n)+p n−1(z)f (n−1)+. . .+p s+1(z)f (s+1)+ . . . + p 0(z)f = 0 have a branching point at infinity (e.g., a logarithmic singularity) and that the coefficients p j , j = s+1, . . . ,n−1, increase slower (in terms of the Nevanlinna characteristics) than p s (z). It is proved that this equation has at most s linearly independent solutions of finite order.

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Authors and Affiliations

  1. “Lvivs’ka Politekhnika” National University, Lviv, Ukraine

    A. A. Mokhon’ko & A. Z. Mokhon’ko

Authors
  1. A. A. Mokhon’ko
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  2. A. Z. Mokhon’ko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 139, pp. 139–144, January, 2014.

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Mokhon’ko, A.A., Mokhon’ko, A.Z. On the Order of Growth of the Solutions of Linear Differential Equations in the Vicinity of a Branching Point. Ukr Math J 67, 159–165 (2015). https://doi.org/10.1007/s11253-015-1071-7

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  • DOI: https://doi.org/10.1007/s11253-015-1071-7

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