Acta mathematica scientia, Series B >
A RESULT OF SYSTEMS OF NONLINEAR COMPLEX ALGEBRAIC DIFFERENTIAL EQUATIONS
Received date: 2008-08-29
Online published: 2010-09-20
Supported by
Project Supported by the Natural Science Foundation of China (10471065)and the Natural Science Foundation of Guangdong Province (04010474).
In this article, we mainly investigate the behavior of systems of complex differential equations when we add some condition to the quality of the
solutions, and obtain an interesting result, which extends Gackstatter and Laine's result concerning complex differential equations to the
systems of algebraic differential equations.
Key words: admissible solution; behavior; complex differential equations
GAO Ling-Yun . A RESULT OF SYSTEMS OF NONLINEAR COMPLEX ALGEBRAIC DIFFERENTIAL EQUATIONS[J]. Acta mathematica scientia, Series B, 2010 , 30(5) : 1507 -1513 . DOI: 10.1016/S0252-9602(10)60143-9
[1] Yang Lo. Value Distribution Theory. Berlin: Springer-Verlag, 1993
[2] He Yuzan, Xiao Xiuzhi. Algebroid Functions and Ordinary Differential Equations. Beijing: Science Press, 1988 (in Chinese)
[3] Gackstatter F, Laine I. Zur Theorie der gewohnlichen differentialgleichungen im komplexen. Ann Polon Math, 1980, 38: 259--287
[4] Toda N. On the growth of meromorphic solutions of some higher order differential equations. J Math Soc Japan, 1986, 38(3): 439--451
[5] He Yuzan, Laine I. The Hayman-Miles Theorem and the differential equation (y')n=R(z, y). Analysis, 1990, 10: 387--396
[6] Ishizaki K, Wang Yuefei. Non-linear differential equations with transcendental meromorphic solutions. J Aust Math Soc, 2001, 70(1): 88--118
[7] Frank G, Wang Yuefei. On the meromorphic solutions of algebraic differential equations. Analysis, 1998, 18(1): 49--54
[8] Yosida K. On algebroid-solutions of ordinary differential equations. Japan J Math, 1934, 10: 199--208
[9] Mokhon`ko A Z. Estimates of Nevanlinna characteristics of algebroid functions and their applications to differential equations. Sib Math Z, 1982, 23: 80--88
[10] He Yuzan. On algebroid solutions of ordinary differential equations. Acta Math Sinica, 1981, 24: 464--471
[11] Xiao Xiuzhi, He Yuzan. Meromorphic and algebroid solutions of higher-order algebraic differential equations. Sci China (Series A), 1983, 10: 1034--1043
[12] Chen Tewei. One class of ordinary differential equations which possess algebroid solutions in the complex domain. Chinese Quarterly J of Math, 1991, 6(4): 45--51
[13] He Yuzan, Xiao Xiuzhi. Admissible solutions and ordinary differential equations. Contemporary Math, 1983, 25: 51--61
[14] Toda N, Kato M. On some algebraic differential equations with admissible algebroid solutions. Proc Japan Acad, Ser A, 1985, 61: 325--328
[15] Baesch A, Steinmetz N. Exceptional solutions of nth order periodic linear differential equations. Complex Variables Theory Appl, 1997, 34(1): 7--17
[16] Steinmetz N. Meromorphic solutions of second-order algebraic differential equations. Complex Variables Theory Appl, 1989, 13(1): 75--83
[17] Steinmetz N. Exceptional values of solutions of linear differential equations. Math Z, 1989, 201(3): 317--326
[18] Heittokangas J, Korhonen R, Laine I. On meromorphic solutions of certain nonlinear differential equations. Bull Austral Math Soc, 2002, 66(2): 331--343
[19] Heittokangas J, et al. Complex difference equations of Malmquist type. Comput Methods Funct Theory, 2001, 1(1): 27--39
[20] Laine I, Yang Ronghua. Finite order solutions of complex linear differential equations. Electron J Differential Equations 2004, 65: 8 (electronic)
[21] Chen Zongxuan, Shon Kwang Ho. On the growth of solutions of a class of higher order differential equations. Acta Mathematica Scientia, 2004, 24B(1): 52--60
[22] Gao Lingyun. Some results of algebroid solutions of complex algebraic differential equations. Indian J Pure and Appl Math, 2001, 32(7): 1041--1050
[23] Gao Lingyun. On the growth of solutions of higher-order differential equations. Acta Mathematica Scientia, 2002, 22B(4): 459--465
[24] Gao Lingyun. Meromorphic admissible solution of ordinary differential equations. Chinese Ann Math, 1999, 20(2): 221--228 (Meromorphic admissible solutions of ordinary differential equations. Contemporary Math, 1999, 20(2): 273--280)
[25] Tu Zhenhan, Xiao Xiuzhi. On the meromorphic solutions of system of higher-order algebraic differential equations. Complex Variables, 1990, 15: 197--209
[26] Song Shugang. Meromorphic solutions of differential equations in the complex domain. Acta Math Sinica, 1991, 34: 779--784 (in Chinese)
[27] Gao Lingyun. The growth of solutions of systems of complex nonlinear algebraic differential equations. Acta Mathematica Scientia, 2010, 30B(3): 932--938
[28] Gao Lingyun. On admissible solution of two types of systems of complex differential equations. Acta Math Sinica, 2000, 43(1): 149--156 (in Chinese)
[29] Gao Lingyun. On $m$ admissible components of solutions. Complex Variables, 1998, 35: 297--306
[30] Gao Lingyun, Sun Daochun, Xiao Xiuzhi. $m$-entire admissible solutions of a type of a system of algebraic differential equations. Kyungpook Math J, 1998, 38(2): 341--350
[31] Gao Lingyun. On the growth of components of meromorphic solutions of systems of complex algebraic differential equations. Acta Mathematicae Applicatae Sinica, 2005, 21(3): 499--504
[32] Li Jianshun. On entire functions which are solutions of quasi-algebraic differential equations of first order. J of Math, 1982, 2(1): 93--104 (in Chinese)
[33] Li Jianshun. Meromorphic solutions of system of algebraic differential equations. J of Math, 1983, 3(2): 173--179 (in Chinese)
[34] Li Kamshun, Chan Waileung. Meromorphic solutions of higher order systems of algebraic differential equations. Math Scand, 1992, 71(1): 105--121
[35] Hayman W K. Meromorphic Functions. Oxford: Clarendon Press, 1964
/
| 〈 |
|
〉 |