Acta mathematica scientia, Series B >
THE GROWTH ORDER OF SOLUTIONS OF SYSTEMS OF COMPLEX DIFFERENCE EQUATIONS
Received date: 2012-03-05
Revised date: 2012-10-02
Online published: 2013-05-20
Supported by
The project is supported by the Natural Science Foundation of China (10471065) and the Natural Science Foundation of Guangdong Province (04010474).
Using Nevanlinna theory of the value distribution of meromorphic functions and Wiman-Valiron theory of entire functions, we investigate the problem of growth order of solutions of a type of systems of difference equations, and extend some results of the growth order of solutions of systems of differential equations to systems of difference equat
Key words： Growth order; difference equations; entire function
GAO Ling-Yun . THE GROWTH ORDER OF SOLUTIONS OF SYSTEMS OF COMPLEX DIFFERENCE EQUATIONS[J]. Acta mathematica scientia, Series B, 2013 , 33(3) : 814 -820 . DOI: 10.1016/S0252-9602(13)60040-5
[1] Yi Hongxun, Yang C C. Theory of the uniqueness of meromorphic functions (in Chinese). Beijing: Science Press, 1995
[2] Laine I. Nevanlinna theory and complex differential equations. Berlin: Walter de Gruyter, 1993
[3] Bank S, Kaufman R. On meromorphic solutions of first-order differential equations. Comment Math Helv, 1976, 51: 289–299
[4] Barsegian G. Estimates of derivatives of meromorphic functions on set of a-points. J London Math Soc, 1986, 34(2): 534–540
[5] Gol’dberg A A. On single-valued solutions of algebraic differential equations. Ukrain Mat Zh, 1956, 8: 254–261
[6] Hayman W K. The growth of solutions of algebraic differential equations. Rend Mat Acc Lincei, 1996, 7: 67–73
[7] Bergweiler W. On a theorem of Gol’dberg concerning meromorphic solutions of algebraic differential equa-tions. Complex Variables, 1998, 37: 93–96
[8] Frank G, Wang Yuefei. On the meromorphic solutions of algebraic differential equations. Analysis, 1998, 18: 49–54
[9] Zalcman L. Normal families:New perspectives. Bull Amer Math Soc, 1998, 35: 215–230
[10] Korhonen R. Meromorphic solutions of differential and difference equations with deficiencies [Ph D Thesis]. Helsinki: Ann Acad Sci Fenn, 2002: 129
[11] Gao Lingyun. The growth of solutions of systems of complex nonlinear algebraic differential equations. Acta Mathematica Scientia, 2010, 30B(3): 932–938
[12] Gao Lingyun. Systems of complex difference equations of Malmquist type. Acta Mathematica Sinica, 2012, 55(2): 293–300
[13] Gao Lingyun. On meromorphic solutions of a type of system of composite functional equations. Acta Mathematica Scientia, 2012, 32B(2): 800–806
[14] Chiang YM, Feng S J. On the growth of logarithmic diffrences, diffrence quo-tients and logarithmic deriva-tives of meromorphic functions. Trans Amer Math Soc, 2009, 361: 3767–3791
/
| 〈 |
|
〉 |