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On algebroid solutions of linear differential equations with algebroid coefficients

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Abstract

We establish a relationship between the growth rates of algebroid solutions and coefficients of nth-order linear differential equations.

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References

  1. Frei, M., Über die Lösungen linearer Differentialgleichungen mit ganzen Funktionen als Koeffizienten, Comment. Math. Helv., 1961, vol. 35, pp. 201–222.

    Article  MATH  MathSciNet  Google Scholar 

  2. Gol’dberg, A.A. and Ostrovskii, I.V., Raspredelenie znachenii meromorfnykh funktsii (The Distribution of Values of Meromorphic Functions), Moscow: Nauka, 1970.

    Google Scholar 

  3. Mokhon’ko, A.Z., The Field of Algebroid Functions and Estimates of Their Nevanlinna Characteristics, Sibirsk. Mat. Zh., 1981, vol. 22, no. 3, pp. 214–218.

    MATH  MathSciNet  Google Scholar 

  4. Valiron, G., Sur la dérivée des fonctions algébroides, Bull. Soc. Math. France, 1931, vol. 59, no. 1–2, pp. 17–39.

    MathSciNet  Google Scholar 

  5. Mokhon’ko, V.D., Lemma on a Logarithmic Derivative for Algebroid Functions, in Teoriya funktsii, funkts. analiz i ikh prilozheniya (Theory of Functions, Functional Analysis, and Their Applications), Kharkov, 1974, no. 20, pp. 112–121.

  6. Ullrich, E., Über den Einfluss der Verzweigtheit einer Algebroide auf ihre Wertverteilung, J. Reine Angew. Math., 1932, vol. 167, pp. 198–220.

    Google Scholar 

  7. Hayman, W.K., Meromorphic Functions, Oxford: Clarendon, 1964. Translated under the title Meromorfnye funktsii, Moscow: Mir, 1966.

    MATH  Google Scholar 

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Original Russian Text © A.Z. Mokhon’ko, L.I. Kolyasa, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 8, pp. 1102–1107.

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Mokhon’ko, A.Z., Kolyasa, L.I. On algebroid solutions of linear differential equations with algebroid coefficients. Diff Equat 45, 1124–1129 (2009). https://doi.org/10.1134/S0012266109080047

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  • DOI: https://doi.org/10.1134/S0012266109080047

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