On meromorphic solutions to the systems of linear differential equations with meromorphic coefficients
Abstract
UDC 517.925.7
For systems of linear differential equations allowing dimension reduction, we obtain estimates of growth rate for meromorphic vector solutions assuming no additional constraints on the growth order of the system coefficients.
References
W. Hengartner, Über die Wachstumsordnung eines linearen Systems von Differentialgleichungen mit ganzen Funktionen als Koeffizienten. (German), Comment. math. helv., 42, № 1, 60 – 80 (1967), https://doi.org/10.1007/BF02564411 DOI: https://doi.org/10.1007/BF02564411
N. Steinmetz, Nevanlinna theory, normal families, and algebraic differential equations, Springer Intern. Publ.. AG (2017), https://doi.org/10.1007/978-3-319-59800-0 DOI: https://doi.org/10.1007/978-3-319-59800-0
A. A. Mohon'ko, Teorema Mal'mkvista dlya reshenij differencial'nyh uravnenij v okrestnosti logarifmicheskoj osoboj tochki, Ukr. mat. zhurn., 56, № 4, 476 – 483 (2004).
A. A. Gol'dberg, I. V. Ostrovskij, Raspredelenie znachenij meromorfnyh funkcij, Nauka, Moskva (1970).
A. Z. Mohon'ko, V. D. Mohon'ko, Ocenki nevanlinnovskih harakteristik nekotoryh klassov meromorfnyh funkcij i ih prilozheniya k differencial'nym uravneniyam, Sib. mat. zhurn.,15, № 6, 1305 – 1322 (1974).
A. Z. Mohon'ko, Pole algebroidnyh funkcij i ocenki ih nevanlinnovskih harakteristik, Sib. mat. zhurn., 22, № 3, 213 – 218 (1981).
U. K. Heĭman, Мероморфные функции. (Russian) [[Meromorphic functions]], Mir, Moscow (1966).
Copyright (c) 2022 А. З. Мохонько, А. А. Мохонько
This work is licensed under a Creative Commons Attribution 4.0 International License.
