On meromorphic solutions to the systems of linear differential equations with meromorphic coefficients

  • A. A. Mokhonko Lviv Polytechnic National University
  • A. Z. Mokhonko Lviv Polytechnic National University
Keywords: .

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.

 

Author Biography

A. A. Mokhonko , Lviv Polytechnic National University

 

 

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).

Published
24.01.2022
How to Cite
Mokhonko A. A., and Mokhonko A. Z. “On Meromorphic Solutions to the Systems of Linear Differential Equations With Meromorphic Coefficients”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 1, Jan. 2022, pp. 99 - 112, doi:10.37863/umzh.v74i1.220.
Section
Research articles