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A Note on Meromorphic Functions with Finite Order and of Bounded l-Index

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Abstract

We present a generalization of concept of bounded l-index for meromorphic functions of finite order. Using known results for entire functions of bounded l-index we obtain similar propositions for meromorphic functions. There are presented analogs of Hayman’s theorem and logarithmic criterion for this class. The propositions are widely used to investigate l-index boundedness of entire solutions of differential equations. Taking this into account we raise a general problem of generalization of some results from theory of entire functions of bounded l-index by meromorphic functions of finite order and their applications to meromorphic solutions of differential equations. There are deduced sufficient conditions providing l-index boundedness of meromoprhic solutions of finite order for the Riccati differential equation. Also we proved that the Weierstrass ℘-function has bounded l-index with l(z) = |z|

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Authors and Affiliations

  1. Department of Advanced Mathematics, Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine

    Andriy Bandura

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  1. Andriy Bandura
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Correspondence to Andriy Bandura.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 18, No. 1, pp. 1–11, January–March, 2021.

This research was supported by the National Research Foundation of Ukraine, 2020.02/0025, 0120U103996.

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Bandura, A. A Note on Meromorphic Functions with Finite Order and of Bounded l-Index. J Math Sci 256, 727–734 (2021). https://doi.org/10.1007/s10958-021-05456-6

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  • DOI: https://doi.org/10.1007/s10958-021-05456-6

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