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Yang, Lian-Zhong

Solution of a differential equation and its applications. (English) Zbl 1004.30021

Kodai Math. J. 22, No. 3, 458-464 (1999).
The author proves that every solution of differential equation \(f^{(k)}-e^{Q(z)}f=1\) (\(k\geq 1\), Q is a nonconstant polynomial) is an entire function of infinite order. He gives some applications of this result.
Reviewer: Anatoly Filip Grishin (Khar’kov)

Cited in 5 Reviews
Cited in 37 Documents

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D20 Entire functions of one complex variable (general theory)

Keywords:

entire function; shared value; uniqueness theorem
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\textit{L.-Z. Yang}, Kodai Math. J. 22, No. 3, 458--464 (1999; Zbl 1004.30021)
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References:

[1] R. BRUCK, On entire functions which share one value CM with their first derivative, Results Math., 30 (1996), 21-24. · Zbl 0861.30032
[2] G. GUNDERSEN, Estimates for the logarithmic derivative of a meromorphic function, plu similar estimates, J. London Math. Soc. (2), 37 (1988), 88-104. · Zbl 0638.30030
[3] W. K. HAYMAN, Meromorphic Functions, Clarendon Press, Oxford, 1964 · Zbl 0115.06203
[4] G. JANK, E. MUES, AND L. VOLKMANN, Meromorphe Funktionen, die mit ihrer ersten un zweiten Ableitung einen endlichen Wert teilen, Complex Variables Theory Appl., 6 (1986), 51-71. · Zbl 0603.30037
[5] A. MARKUSHEVICH, Theory of Functions of a Complex Variable, Volume 2, translated b R. Silverman, Prenctice-Hall, Englewood Cliffs, 1965.
[6] L. RUBEL AND C. C. YANG, Values shared by an entire function and its derivative, Comple Analysis, Lecture Notes in Math., 599, Springer-Verlag, Berlin, 1977, 101-103. · Zbl 0362.30026
[7] H. X. Yi AND C. C. YANG, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, 1995, in Chinese
[8] Q. C. ZHANG, The uniqueness of meromorphic functions with their derivatives, Kodai Math J., 21 (1998), 179-184. · Zbl 0932.30027
[9] H. ZHONG, Entire functions that share one value with their derivatives, Kodai Math. J., 1 (1995), 250-259. · Zbl 0840.30013
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