JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON THE TRANSCENDENTAL ENTIRE SOLUTIONS OF A CLASS OF DIFFERENTIAL EQUATIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON THE TRANSCENDENTAL ENTIRE SOLUTIONS OF A CLASS OF DIFFERENTIAL EQUATIONS
Lu, Weiran; Li, Qiuying; Yang, Chungchun;
  PDF(new window)
 Abstract
In this paper, we consider the differential equation , where and are polynomials with , R is a rational function and is an entire function. We consider solutions of the form , where f is an entire function and is an integer, and we prove that if f is a transcendental entire function, then is a polynomial and . This theorem improves some known results and answers an open question raised in [16].
 Keywords
transcendental entire solutions;differential equation;Nevanlinna theory;
 Language
English
 Cited by
1.
A RESULT ON A CONJECTURE OF W. LÜ, Q. LI AND C. YANG, Bulletin of the Korean Mathematical Society, 2016, 53, 2, 411  crossref(new windwow)
 References
1.
R. Bruck, On entire functions which share one value CM with their first derivatives, Results Math. 30 (1996), no. 1-2, 21-24. crossref(new window)

2.
Z. X. Chen and K. H. Shon, On conjecture of R. Bruck concerning the entire function sharing one value CM with its derivative, Taiwanese J. Math. 8 (2004), no. 2, 235-244.

3.
J. Clunie, On integral and meromorphic functions, J. London Math. Soc. 37 (1962), 17-22.

4.
W. Doeringer, Exceptional value of differential polynomials, Pacific J. Math. 98 (1982), no. 1, 55-52. crossref(new window)

5.
G. G. Gundersen and L. Z. Yang, Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl. 223 (1998), no. 1, 88-95. crossref(new window)

6.
W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.

7.
I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, 1993.

8.
C. L. Lei, M. L. Fang, et al., A note on unicity of meromorophic functions, Acta Math. Sci. Ser. A. Chin. Ed. 28 (2008), no. 5, 802-807.

9.
F. Lu, A note on the Bruck conjecture, Bull. Korean Math. Soc. 48 (2011), no. 5, 951-957. crossref(new window)

10.
F. Lu and H. X. Yi, The Bruck conjecture and entire functions sharing polynomals with their k−th derivatives, J. Korean Math. Soc. 48 (2011), no. 3, 499-512. crossref(new window)

11.
E. Mues and N. Steinmetz, Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen, Manuscripta Math. 29 (1979), no. 2-4, 195-206. crossref(new window)

12.
L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, Complex Analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), 101-103, Lecture Notes in Math., Vol. 599, Springer, Berlin, 1977.

13.
L. Z. Yang and J. L. Zhang, Non-existence of meromorphic solutions of a Fermat type functional equation, Aequationes Math. 76 (2008), no. 1-2, 140-150. crossref(new window)

14.
H. X. Yi and C. C. Yang, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, 1995.

15.
J. L. Zhang and L. Z. Yang, A power of an entire function sharing one value with its derivative, Comput. Math. Appl. 60 (2010), no. 7, 2153-2160. crossref(new window)

16.
J. L. Zhang and L. Z. Yang, A power of a meromorphic function sharing a small function with its derivative, Ann. Acad. Sci. Fenn. Math. 34 (2009), no. 1, 249-260.

17.
T. D. Zhang and W. R. Lu, Notes on a meromorphic function sharing one small function with its derivative, Complex Var. Elliptic Equ. 53 (2008), no. 9, 857-867. crossref(new window)