[1] Zhu Lingmei, Yang Degui, Wang Xiaoling, On the growth of transcendental entiresolutions of algebraic differential equations [J]. Journal of Southeast University (English Edition), 2003, 19 (1): 98-102. [doi:10.3969/j.issn.1003-7985.2003.01.022]

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On the growth of transcendental entiresolutions of algebraic differential equations()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

19

Issue:

2003 1

Page:

98-102

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2003-03-30

Info

Title:

On the growth of transcendental entiresolutions of algebraic differential equations

Author(s):

Zhu Lingmei¹;  Yang Degui²;  Wang Xiaoling¹;  3

¹Department of Applied Mathematics, Nanjing University of Economics, Nanjing 210003, China
²College of Sciences, South China Agricultural University, Guangzhou 510642, China
³Department of Mathematics, The Hong Kon

Keywords:

algebraic differential equation;  degree;  entire solutions

PACS:

O174.5

DOI:

10.3969/j.issn.1003-7985.2003.01.022

Abstract:

In this paper, we investigate the growth of transcendental entire solutions of the following algebraic differential equation a(z)f ′²+(b₂(z)f 2+b₁(z)f+b₀(z))f ′=d₃(z)f 3+d₂(z)f 2+d₁(z)f+d₀(z), where a(z), b_i(z)(0≤i≤2) and d_j(z)(0≤j≤3) are all polynomials, and this equation relates closely to the following well-known algebraic differential equation C(z, w)w′²+B(z, w)w′+A(z, w)=0, where C(z, w)≢0, B(z, w) and A(z, w) are three polynomials in z and w. We give relationships between the growth of entire solutions and the degrees of the above three polynomials in detail.

References:

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[2] Ishizaki I. A result for a certain algebraic differential equation[J]. Bull Hong Kong Math Soc, 1997, 1(2): 301-308.
[3] Steinmetz N. Ein Malmquistscher satz fur algebraische differentialgleichungen erster ordnung[J]. J Reine Angew Math, 1980, 316(1): 44-53.
[4] He Y Z, Xiao X Z. Algebroid functions and ordinary differential equations[M]. Beijing: Science Press, 1988. 18-19.(in Chinese)
[5] Laine I. Nevanlinna theory and complex differential equations[M]. Berlin, New York: Walter de Gruyter, 1993. 50-52.
[6] Jank G, Volkmann L. Einfuhrung in die theorie der ganzen und meromorphen funktionen mit anwendungen auf differentialgleichungen[M]. Basel-Boston: Birkhauser, 1985. 36-37.
[7] Goldberg A A. On single-valued solutions of first-order differential equations[J]. Ukrain Mat Zh, 1956, 8(2): 254-261.
[8] Strelitz S. Three theorems on the growth of entire transcendental solutions of algebraic differential equations[J]. Canad J Math, 1983, 35(6): 1110-1128.
[9] Hayman W K. The growth of solutions of algebraic differential equations[J]. Rend Mat Accad Lincei, 1996, 7(1): 67-73.

Memo

Memo:

Biography: Zhu Lingmei(1950—), female, associate professor, zhulm@njue.edu.cn.

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