Unfoldings of Meromorphic Functions.
Tatsuo Suwa (1983)
Mathematische Annalen
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Tatsuo Suwa (1983)
Mathematische Annalen
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Habib Habib, Benharrat Belaïdi (2013)
Annales Polonici Mathematici
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We investigate the growth and fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives. Our results extend the previous results due to Peng and Chen.
S.K. SINGH, H.S. GOPALAKRISHNA (1971)
Mathematische Annalen
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S.H. DWIVEDI (1971)
Mathematische Annalen
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I. Lahiri (1989)
Matematički Vesnik
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S. K. Bajpai, T. J. S. Mehrok (1975)
Annales Polonici Mathematici
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H. S. Gopalakrishna, Subhas S. Bhoosnurmath (1976)
Annales Polonici Mathematici
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Hong-Yan Xu, Xiu-Min Zheng, Hua Wang (2016)
Open Mathematics
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In this article, we study the uniqueness problem of meromorphic functions in m-punctured complex plane Ω and obtain that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 9, such that any two admissible meromorphic functions f and g in Ω must be identical if f, g share S1, S2 I M in Ω.
Xiao-Min Li, Hong-Xun Yi (2010)
Annales Polonici Mathematici
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We prove some uniqueness theorems for meromorphic functions and their derivatives that share a meromorphic function whose order is less than those of the above meromorphic functions. The results in this paper improve those given by G. G. Gundersen & L. Z. Yang, J. P. Wang, J. M. Chang & Y. Z. Zhu, and others. Some examples are provided to show that our results are the best possible.
Hong Yan Xu, San Yang Liu (2017)
Open Mathematics
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The main purpose of this paper is to investigate the uniqueness of meromorphic functions that share two finite sets in the k-punctured complex plane. It is proved that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 5, such that any two admissible meromorphic functions f and g in Ω must be identical if EΩ(Sj, f) = EΩ(Sj, g)(j = 1,2).
Yuxian Chen, Zhaojun Wu (2012)
Annales Polonici Mathematici
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This paper is devoted to exceptional values of meromorphic functions and of their derivatives on annuli. Some facts on exceptional values for meromorphic functions in the complex plane which were established by Singh, Gopalakrishna and Bhoosnurmath [Math. Ann. 191 (1971), 121-142, and Ann. Polon. Math. 35 (1977/78), 99-105] will be considered on annuli.
H. S. Gopalakrishna, Subhas S. Bhoosnurmath (1977)
Annales Polonici Mathematici
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El Farissi, A., Belaidi, B. (2009)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Domínguez, Patricia (1998)
Annales Academiae Scientiarum Fennicae. Mathematica
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Wang, Songmin, Gao, Zongsheng (2007)
Abstract and Applied Analysis
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Jun-Fan Chen (2017)
Open Mathematics
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We prove uniqueness theorems of meromorphic functions, which show how two meromorphic functions are uniquely determined by their two finite shared sets. This answers a question posed by Gross. Moreover, some examples are provided to demonstrate that all the conditions are necessary.
S. K. Singh, V. N. Kulkarni (1973)
Annales Polonici Mathematici
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Ran Ran Zhang, Zong Xuan Chen (2010)
Annales Polonici Mathematici
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We investigate the growth and Borel exceptional values of meromorphic solutions of the Riccati differential equation w' = a(z) + b(z)w + w², where a(z) and b(z) are meromorphic functions. In particular, we correct a result of E. Hille [Ordinary Differential Equations in the Complex Domain, 1976] and get a precise estimate on the growth order of the transcendental meromorphic solution w(z); and if at least one of a(z) and b(z) is non-constant, then we...
Wei-Ran Lü, Hong-Xun Yi (2003)
Annales Polonici Mathematici
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We deal with the problem of uniqueness of meromorphic functions sharing three values, and obtain several results which improve and extend some theorems of M. Ozawa, H. Ueda, H. X. Yi and other authors. We provide examples to show that results are sharp.