Abstract
This paper is devoted to studying the uniqueness problem of entire functions sharing a small function with their linear differential polynomials.
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References
A. Al-Khaladi, On meromorphic functions that share one value with their derivative, Analysis 25 (2005), 131–140.
R. Brück, On entire functions which share one value CM with their first derivative, Results Math. 30 (1996), 21–24.
J. Chang and M. Fang, Uniqueness of entire functions, J. Math. Anal. Appl. 288 (2003), 97–111.
J. Chang and M. Fang, Entire functions that share a small functions with their derivatives, Complex Variables Theory Appl. 49 (2004), 871–895.
Z. Chen and K. Shon, On conjecture of R. Brück concerning the entire function sharing one value CM with its derivative, Taiwanese J. Math. 8 (2004), 235–244.
J. Clunie, The composition of entire and meromorphic functions, Mathematical Essays Dedicated to A. J. Macintyre, Ohio Univ. Press, Athens, Ohio, 1970, 75–92.
G. Gundersen and L. Yang, Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl. 223 (1998), 88–95.
W. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
S. Hellerstein and L. Rubel, Subfields that are algebraically closed in the field of all meromorphic functions, J. Analyse Math. 12 (1964), 105–111.
G. Jank and L. Volkmann, Einführung in die Theorie der ganzen und meromorphen Funktionen mit Anwendungen auf Differentialgleichungen, Birkhäuser, Basel-Boston, 1985.
P. Li and C.-C. Yang, Uniqueness theorems on entire functions and their derivatives, J. Math. Anal. Appl. 253 (2001), 50–57.
A. Mohon’ko, The Nevanlinna characteristics of certain meromorphic functions, (in Russian) Teor. Funktsiĭ Funktional. Anal. i Prilozhen. 14 (1971), 83–87.
N. Steinmetz, Zur Wertverteilung von Exponentialpolynomen, Manuscripta Math. 26 (1978/79), 155–167.
J. Wang and Y. Li, Oscillation result for some non-homogeneous linear differential equations and its application, Acta Math. Appl. Sin. Engl. Ser. 21 (2005), 381–388.
W. Wang and P. Li, Unicity of entire functions and their linear differential polynomials, Complex Variables Theory Appl. 49 (2004), 821–832.
L. Z. Yang, Further results on entire functions that share one value with their derivatives, J. Math. Anal. Appl. 212 (1997), 529–536.
L. Z. Yang, Solution of a differential equation and its application, Kodai Math. J. 22 (1999), 458–464.
H. X. Yi and C. C. Yang, Uniqueness Theory of Meromorphic Functions, Mathematics and Its Applications, Science Press/Kluwer Acad. Publ., 2003.
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The first author has been partially sponsored by Shanghai Postdoctoral Scientific Program and the second author has been partially supported by the Academy of Finland grant 210245.
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Wang, J., Laine, I. Uniqueness of Entire Functions and Their Derivatives. Comput. Methods Funct. Theory 8, 327–338 (2008). https://doi.org/10.1007/BF03321691
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DOI: https://doi.org/10.1007/BF03321691