JOURNAL BROWSE
Search
Advanced SearchSearch Tips
RADIAL OSCILLATION OF LINEAR DIFFERENTIAL EQUATION
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
RADIAL OSCILLATION OF LINEAR DIFFERENTIAL EQUATION
Wu, Zhaojun;
  PDF(new window)
 Abstract
In this paper, the radial oscillation of the solutions of higher order homogeneous linear differential equation $$f^{(k)}+A_{n-2}(z)f^{(k-2)}+{\cdots}+A_1(z)f^{\prime}+A_0(z)f
 Keywords
radial exponent of convergence;iterated order;sectorial oscillation;Borel direction;
 Language
English
 Cited by
1.
Sectorial oscillation theory of linear differential equations, Acta Mathematica Scientia, 2013, 33, 4, 1177  crossref(new windwow)
 References
1.
S. B. Bank and I. Laine, On the oscillation theory of f'' + Af = 0 where A is entire, Trans. Amer. Math. Soc. 273 (1982), no. 1, 351-363.

2.
S. B. Bank and J. K. Langley, Oscillation theory for higher order linear differential equations with entire coefficients, Complex Variables Theory Appl. 16 (1991), no. 2-3, 163-175. crossref(new window)

3.
L. G. Bernal, On growth k-order of solutions of a complex homogeneous linear differ- ential equation, Proc. Amer. Math. Soc. 101 (1987), no. 2, 317-322.

4.
T.-B. Cao, Complex oscillation of entire solutions of higher-order linear differential equations, Electron. J. Differential Equations 2006 (2006), no. 81, 8 pp. (electronic).

5.
C. Chuang, Differential Polynomials of Meromorphic Functions, Beijing Normal University Press, Beijing, 1999.

6.
S. Gao, Z. Chen, and T. Chen, Oscillation Theory of Linear Differential Equation, Huazhong University of Science and Technology Press, Wuhan, 1998.

7.
Z. Huang and Z. Chen, Angular distribution with hyper-order in complex oscillation theory, Acta Math. Sinica (Chin. Ser.) 50 (2007), no. 3, 601-614.

8.
Z. Huang and Z. Chen, The zeros distribution of solutions of higher order differential equations in an angular domain, Bull. Korean Math. Soc. 47 (2010), no. 3, 443-454. crossref(new window)

9.
Z. Huang and Z. Chen, The zeros distribution of hyper solutions of higher order differential equations in angular domain, Southeast Asian Bull. Math. 34 (2010), no. 3, 429-438.

10.
G. Jank and L. Volkmann, Meromorphe funktionen und Differentialiagleichungen, Birkhauser, 1985.

11.
L. Kinnunen, Linear differential equations with solutions of finite iterated order, Southeast Asian Bull. Math. 22 (1998), no. 4, 385-405.

12.
I. Laine, Nevanlinna theory and complex differential equations, de Gruyter Studies in Mathematics, 15. Walter de Gruyter Co., Berlin, 1993.

13.
R. Nevanlinna, uber eine Klasse meromorpher Funktionen, Math. Ann. 92 (1924), no. 3-4, 145-154. crossref(new window)

14.
J. Rossi and S. Wang, The radial oscillation of solutions to ODE's in the complex domain, Proc. Edinburgh Math. Soc. (2) 39 (1996), no. 3, 473-483. crossref(new window)

15.
D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc. 69 (1963), 411-414. crossref(new window)

16.
M. Tsuji, Potential Theory in Modern Function Theory, Maruzen Co. Ltd, Tokyo, 1959.

17.
S. Wang, On the sectorial oscillation theory of f'' + A(z)f = 0, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes (1994), no. 92, 66 pp.

18.
S. Wu, Angular distribution in complex oscillation, Sci. China Ser. A 48 (2005), no. 1, 107-114.

19.
S. Wu, On the location of zeros of solution of f'' +Af = 0 where A(z) is entire, Math. Scand. 74 (1994), no. 2, 293-312.

20.
Z. Wu and D. Sun, Angular distribution of solutions of higher order linear differential equations, J. Korean Math. Soc. 44 (2007), no. 6, 1329-1338. crossref(new window)

21.
Z. Wu and D. Sun, Sectorial oscillation of linear differential equations and iterated order, Electron. J. Differential Equations 2007 (2007), no. 134, 7 pp. (electronic).

22.
L. Yang, Value Distribution Theory, Translated and revised from the 1982 Chinese original. Springer-Verlag, Berlin; Science Press Beijing, Beijing, 1993.

23.
C. Yi, The augular distribution of the solutions of higher order differential equation, Acta Math. Sinica (Chin. Ser.) 48 (2005), no. 1, 133-140.

24.
J. Zheng, Value Distrbution of Meromorphic Functions, Springer, Beijing: Tsinghua Univ. Press. 2010.