Fast growing meromorphic solutions of the systems of linear
differential equations

A. Z. Mokhonko; A. A. Mokhonko

doi:10.15330/ms.50.2.158-172

Systems of linear differential equations that allow for dimension decrease are considered. Growth estimates for meromorphic vector-solutions are obtained. An essentially new feature is that there are no additional constraints for the growth order of the system coefficients.

1. Golubev V.V. Lectures on analytic theoury of differential equations. - Gostehizdat, Moscow; Leningrad, 1950. - 436 p. (in Russian)

2. Hengartner W. Uber die Wachstumsordnung eines linearen Systems von Differentialgleichungen mit ganzen Funktionen als Koeffizienten// Comment. math. helv. - 1967. - V.42, №1. - P.60-80.

3. Steinmetz N. Nevanlinna Theory, Normal Families, and Algebraic Differential Equations. - Springer International Publishing AG, 2017 - 235p.

4. Chyzhykov I.E., Semochko N.S. Fast growing entire solutions of linear differential equations// Mat. Visnuk NTSh. - 2016. - V.13. - P. 68-83.

5. Mokhonko A.A. Malmquist Theorem for solutions of differential equations in the neigbourhood of logarithmic singularity// Ukrainian Mathematical J. - 2004. - V.56, №4. - P. 476-483. (in Ukrainain)

6. Goldberg A.A., Ostrovskii I.V., Value distribution of meromorphic functions. Translations of Mathematical Monographs, V.236, Springer, Berlin, 2008.

7. A.Z. Mokhonko, V.D. Mokhonko, Estimates for the Nevanlinna characteristics of some classes of meromorphic functions and their applications to differential equations// Sib. Math. J. - 1974. - V.15. - P. 921-934. (in Russian)

8. Mokhonko A.Z. Field of algebroid functions and estimates of their Nevanlinnas characteristics// Siberian Math. J. - 1981. - V.3. - P. 213-218. (in Russian)

9. Schonhage A. Uber das Wachstum der zusammengesetzen Funktionen// Math. Z. - 1960. - V.73. - P. 22-44.

10. Juneja O.P., Kapoor G.P., Bajpai S.K. On the [p; q]-order and lower [p; q]-order of an entire function// J. Reine Angev. Math. - 1976. - V.282. - P. 53-67.

11. Sheremeta M.N. About connection between absolute value of the module of entire function and absolute values of the coefficients of its series expansion// Izvestia Vuzov Mathematica. - 1967. - V.2. - P. 100-108. (in Russian)

12. Bandura A., Skaskiv O., Filevych P. Properties of entire solutions of some linear PDEs// J. Appl. Math. Comput. Nech. - 2017. - V.16., №2, P. 17-28.

13. W.K. Hayman, Meromorphic function, Mir, Moscow, 1966, 287p. (in Russian)

	Fast growing meromorphic solutions of the systems of linear differential equations
Author	A. Z. Mokhonko, A. A. Mokhonko mohon@soft-hitech.com Lviv Polytechnic National University, Lviv, Ukraine
Abstract	Systems of linear differential equations that allow for dimension decrease are considered. Growth estimates for meromorphic vector-solutions are obtained. An essentially new feature is that there are no additional constraints for the growth order of the system coefficients.
Keywords	system; linear differential equations; meromorphic function; entire function; Nevanlinna characteristics; order of growth; scale of growth; logarithmic derivative
DOI	doi:10.15330/ms.50.2.158-172
Reference	1. Golubev V.V. Lectures on analytic theoury of differential equations. - Gostehizdat, Moscow; Leningrad, 1950. - 436 p. (in Russian) 2. Hengartner W. Uber die Wachstumsordnung eines linearen Systems von Differentialgleichungen mit ganzen Funktionen als Koeffizienten// Comment. math. helv. - 1967. - V.42, №1. - P.60-80. 3. Steinmetz N. Nevanlinna Theory, Normal Families, and Algebraic Differential Equations. - Springer International Publishing AG, 2017 - 235p. 4. Chyzhykov I.E., Semochko N.S. Fast growing entire solutions of linear differential equations// Mat. Visnuk NTSh. - 2016. - V.13. - P. 68-83. 5. Mokhonko A.A. Malmquist Theorem for solutions of differential equations in the neigbourhood of logarithmic singularity// Ukrainian Mathematical J. - 2004. - V.56, №4. - P. 476-483. (in Ukrainain) 6. Goldberg A.A., Ostrovskii I.V., Value distribution of meromorphic functions. Translations of Mathematical Monographs, V.236, Springer, Berlin, 2008. 7. A.Z. Mokhonko, V.D. Mokhonko, Estimates for the Nevanlinna characteristics of some classes of meromorphic functions and their applications to differential equations// Sib. Math. J. - 1974. - V.15. - P. 921-934. (in Russian) 8. Mokhonko A.Z. Field of algebroid functions and estimates of their Nevanlinnas characteristics// Siberian Math. J. - 1981. - V.3. - P. 213-218. (in Russian) 9. Schonhage A. Uber das Wachstum der zusammengesetzen Funktionen// Math. Z. - 1960. - V.73. - P. 22-44. 10. Juneja O.P., Kapoor G.P., Bajpai S.K. On the [p; q]-order and lower [p; q]-order of an entire function// J. Reine Angev. Math. - 1976. - V.282. - P. 53-67. 11. Sheremeta M.N. About connection between absolute value of the module of entire function and absolute values of the coefficients of its series expansion// Izvestia Vuzov Mathematica. - 1967. - V.2. - P. 100-108. (in Russian) 12. Bandura A., Skaskiv O., Filevych P. Properties of entire solutions of some linear PDEs// J. Appl. Math. Comput. Nech. - 2017. - V.16., №2, P. 17-28. 13. W.K. Hayman, Meromorphic function, Mir, Moscow, 1966, 287p. (in Russian)
Pages	158-172
Volume	50
Issue	2
Year	2018
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Fast growing meromorphic solutions of the systems of linear differential equations