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[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), bi(z)(0≤i≤2) and dj(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:

[1] Liao L W, Yang C C. On the growth and factorization of entire solutions of algebraic differential equations[J]. Ann Acad Sci Fen Math, 2000, 25(1): 73-84.
[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.
Last Update: 2003-03-20