Evaluation of the growth of solutions of systems of linear differential equations of the nth order

Authors

  • A. Mokhon’ko National University "Lviv Polytechnic"
  • O. Mokhon’ko National University "Lviv Polytechnic"

DOI:

https://doi.org/10.3842/umzh.v77i2.8406

Keywords:

systems of ordinary differential equations, analytic functions, branch point, analytical continuation, Riemann surface, maximum of absolute value

Abstract

UDC 517.925.7

For a system of linear differential equations of the mth order with coefficients holomorphic in a neighborhood of ∞, we obtain an a priori estimate of growth for the n-valued (n∈N) analytic vector solutions of the system via the estimate for the order of growth of its coefficients.

References

1. N. Steinmetz, Nevanlinna theory, normal families, and algebraic differential equations, Springer International Publishing AG (2017). DOI: https://doi.org/10.1007/978-3-319-59800-0

2. Ш. И. Стрелиц, Асимптотические свойства аналитических решений дифференциальных уравнений, Минтас, Вильнюс (1972).

3. A. A. Mokhonko, A. Z. Mokhonko, On meromorphic solutions of the systems of linear differential equations with meromorphic coefficients, Ukr. Math. J., 74, 114–130 (2022); https://doi.org/10.1007/s11253-022-02051-z; https://doi.org/10.1007/s11253-022-02051-z.

4. A. I. Markushevich, Theory of analytical functions, in 2 vol., Nauka, Moscow (1968).

5. А. А. Гольдберг, И. В. Островский, Распределение значений мероморфных функций, Наука, Москва (1970).

6. A. A. Mokhon’ko, A. Z. Mokhon’ko, Malmquist theorem for the solutions of differential equations in the vicinity of a branching point, Ukr. Math. J., 66, 1442–1447 (2015); https://doi.org/10.1007/s11253-015-1024-1; https://doi.org/10.1007/s11253-015-1024-1. DOI: https://doi.org/10.1007/s11253-015-1024-1

7. A. A. Mokhon’ko, A. Z. Mokhon’ko, Deficiency values for the solutions of differential equations with branching point, Ukr. Math. J., 66, 1048–1069 (2014); https://doi.org/10.1007/s11253-014-0994-8; https://doi.org/10.1007/s11253-014-0994-8. DOI: https://doi.org/10.1007/s11253-014-0994-8

Downloads

Published

28.03.2025

Issue

Vol. 77 No. 2 (2025)

Section

Research articles

License

Copyright (c) 2025 Анатолій Мохонько, Олексій Мохонько

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Mokhon’ko, A., and O. Mokhon’ko. “Evaluation of the Growth of Solutions of Systems of Linear Differential Equations of the nth Order”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 2, Mar. 2025, pp. 144–151, https://doi.org/10.3842/umzh.v77i2.8406.