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GROWTH AND FIXED POINTS OF MEROMORPHIC SOLUTIONS OF HIGHER-ORDER LINEAR DIFFERENTIAL EQUATIONS
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 Title & Authors
GROWTH AND FIXED POINTS OF MEROMORPHIC SOLUTIONS OF HIGHER-ORDER LINEAR DIFFERENTIAL EQUATIONS
Xu, Jun-Feng; Yi, Hong-Xun;
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 Abstract
In this paper, we investigate the growth and fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives. Because of the restriction of differential equations, we obtain that the properties of fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives are more interesting than that of general transcendental meromorphic functions. Our results extend the previous results due to M. Frei, M. Ozawa, G. Gundersen, and J. K. Langley and Z. Chen and K. Shon.
 Keywords
linear differential equation;meromorphic function;fixed point;
 Language
English
 Cited by
1.
Growth and fixed points of meromorphic solutions of nonhomogeneous linear differential equations, Advances in Difference Equations, 2013, 2013, 1, 370  crossref(new windwow)
2.
Some results of meromorphic solutions of second-order linear differential equations, Journal of Inequalities and Applications, 2013, 2013, 1, 304  crossref(new windwow)
 References
1.
I. Amemiya and M. Ozawa, Nonexistence of finite order solutions of $w^{''}+ e^{-z}w^'+Q(z)w=0$, Hokkaido Math. J. 10 (1981), Special Issue, 1–17 crossref(new window)

2.
Z. X. Chen, The growth of solutions of differential equation $f^{''}+e^{-z}f^'+Q(z)f=0, Science in China (series A). 31(2001), no.9, 775–784

3.
Z. X. Chen, The fixed points and hyper order of solutions of second order complex differential equations, Acta Math. Sci. Ser. A Chin. Ed. 20 (2000), no. 3, 425–432

4.
Z. X. Chen, Zeros of meromorphic solutions of higher order linear differential equations, Analysis 14 (1994), no. 4, 425–438

5.
Z. X. Chen and K. H. Shon, On the growth and fixed points of solutions of second order differential equations with meromorphic coefficients, Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 4, 753–764 crossref(new window)

6.
Z. X. Chen and K. H. Shon, The growth of solutions of higher order differential equations, Southeast Asian Bull. Math. 27 (2004), no. 6, 995–1004

7.
Z. X. Chen and C. C. Yang, Some further results on the zeros and growths of entire solutions of second order linear differential equations, Kodai Math. J. 22 (1999), no. 2, 273–285 crossref(new window)

8.
M. Frei, Uber die subnormalen Losungen der Differentialgleichung $w^{''}+e^{-z}w'+konst.w=0, Comment. Math. Helv. 36 (1961), 1–8 crossref(new window)

9.
F. Gross, On the distribution of values of meromorphic functions, Trans. Amer. Math. Soc. 131 (1968), 199–214 crossref(new window)

10.
G. Gundersen, On the question of whether $f^{''}+e^{-z}f^'+B(z)f=0$ can admit a solution $f\neq0$ of finite order, Proc. Roy. Soc. Edinburgh Sect. A 102 (1986), no. 1-2, 9–17 crossref(new window)

11.
G. Gundersen, Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J. London Math. Soc. (2) 37 (1988), no. 1, 88–104 crossref(new window)

12.
G. Gundersen, Finite order solutions of second order linear differential equations, Trans. Amer. Math. Soc. 305 (1988), no. 1, 415–429

13.
W. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964

14.
E. Hille, Ordinary Differential Equations in the Complex Domain, Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1976

15.
I. Laine, Nevanlinna Theory and Complex Differential Equations, de Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin, 1993

16.
I. Laine and J. Rieppo, Differential polynomials generated by linear differential equations, Complex Var. Theory Appl. 49 (2004), no. 12, 897–911 crossref(new window)

17.
J. K. Langley, On complex oscillation and a problem of Ozawa, Kodai Math. J. 9 (1986), no. 3, 430–439 crossref(new window)

18.
A. I. Markushevich, Theory of Functions of a Complex Variable, Prentice-Hall, New Jersey, 1965

19.
J. Wang, Oscillation results for solutions of differential equations and their application, Doctoral Thesis, Shandong University, 2003

20.
J.Wang and H. X. Yi, Fixed points and hyper order of differential polynomials generated by solutions of differential equation, Complex Var. Theory Appl. 48 (2003), no. 1, 83–94 crossref(new window)

21.
L. Yang, Value Distribution Theory, Springer, Berlin, Heidelberg, New York, 1993

22.
H. X. Yi and C. C. Yang, The Uniqueness Theory of Meromorphic Functions, Science Press/Kluwer Academic Publishers, Beijing/New York, 2003

23.
Q.T. Zhuang and C. C. Yang, The Fixed Points and Factorization Theory of Meromorphic Functions, Press in Beijing University, Beijing, 1988