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On the uniqueness of an entire function sharing a small entire function with some linear differential polynomial

Xiao-Min Li; Hong-Xun Yi

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 4, page 1039-1058
  • ISSN: 0011-4642

Abstract

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We prove a theorem on the growth of nonconstant solutions of a linear differential equation. From this we obtain some uniqueness theorems concerning that a nonconstant entire function and its linear differential polynomial share a small entire function. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible.

How to cite

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Li, Xiao-Min, and Yi, Hong-Xun. "On the uniqueness of an entire function sharing a small entire function with some linear differential polynomial." Czechoslovak Mathematical Journal 59.4 (2009): 1039-1058. <http://eudml.org/doc/37976>.

@article{Li2009,
abstract = {We prove a theorem on the growth of nonconstant solutions of a linear differential equation. From this we obtain some uniqueness theorems concerning that a nonconstant entire function and its linear differential polynomial share a small entire function. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible.},
author = {Li, Xiao-Min, Yi, Hong-Xun},
journal = {Czechoslovak Mathematical Journal},
keywords = {entire functions; order of growth; shared values; uniqueness theorems; entire function; order of growth; shared values; uniqueness theorem},
language = {eng},
number = {4},
pages = {1039-1058},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the uniqueness of an entire function sharing a small entire function with some linear differential polynomial},
url = {http://eudml.org/doc/37976},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Li, Xiao-Min
AU - Yi, Hong-Xun
TI - On the uniqueness of an entire function sharing a small entire function with some linear differential polynomial
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 4
SP - 1039
EP - 1058
AB - We prove a theorem on the growth of nonconstant solutions of a linear differential equation. From this we obtain some uniqueness theorems concerning that a nonconstant entire function and its linear differential polynomial share a small entire function. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible.
LA - eng
KW - entire functions; order of growth; shared values; uniqueness theorems; entire function; order of growth; shared values; uniqueness theorem
UR - http://eudml.org/doc/37976
ER -

References

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  9. Laine, I., Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter Berlin (1993). (1993) MR1207139
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  11. Rubel, L., Yang, C. C., Values shared by an entire function and its derivative, in``Complex Analysis, Kentucky 1976'' (Proc. Conf.), Lecture Notes in Mathematics, Vol. 599, pp. 101-103, Springer-Verlag, Berlin, 1977. (1977) Zbl0362.30026MR0460640
  12. Valiron, G., Lectures on the General Theory of Integral Functions, Edouarard Privat Toulouse (1923) JFM 50.0254.01. 
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  14. Yang, L., Value Distribution Theory, Springer-Verlag Berlin Heidelberg (1993). (1993) Zbl0790.30018MR1301781
  15. Yang, C. C., Yi, H. X., Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers Dordrecht/Boston/London (2003). (2003) Zbl1070.30011MR2105668
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