Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (3): 732-751.doi: 10.1016/S0252-9602(17)30034-6
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Yue WANG
Received:
2016-01-26
Revised:
2016-06-06
Online:
2017-06-25
Published:
2017-06-25
Supported by:
Yue WANG. MEROMORPHIC SOLUTIONS OF SOME TYPES OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS[J].Acta mathematica scientia,Series B, 2017, 37(3): 732-751.
[1] He Y Z, Xiao X Z. Algebroid functions and ordinary differential equations. Beijing:Science Press, 1988 [2] Laine I. Nevanlinna theory and complex differential equations. Berlin:Walter de Gruyter, 1993 [3] Yi H X, Yang C C. Theory of the uniqueness of meromorphic function. Beijing:Science Press, 1995 [4] Chen Z X. On the rate of growth of meromorphic solutions of higher order differential equations. Acta Mathematica Sinica, 1999, 42(3):551-558 [5] Chen Z X, Shon K H. On the growth of solutions of a class of higher order differential equation. Acta Mathematica Scientia, 2004, 24B(1):52-60 [6] Gao L Y. On the growth of components of meromorphic solutions of systems of complex differential equations. Acta Mathematicae Applicatae Sinica, 2005, 21B(3):499-504 [7] Gao L Y. Expression of meromorphic solutions of systems of algebraic differential equations with exponential coeffents. Acta Mathematica Scientia, 2011, 31B(2):541-548 [8] Gao L Y. Transcendental solutions of systems of complex differential equations. Acta Mathematica Sinica, Chinese Series, 2015, 58(1):41-48 [9] Li K S, Chan W L. Meromorphic solutions of higher order systems of algebraic differential Equations. Math Scand, 1992, 71(1):105-121 [10] Mohon'ko A Z, Mokhon'ko V D. Estimates for the Nevanlinna characteristics of some classes of meromorphic functions and their applications to differential equations. Siirskii Matematicheskii Zhurnal, 1974, 15:1305-1322 [11] Toda N. On algebroid solutions of some binomial differential equations in the complex plane. Proc Japan Acad, 1988, 64A(3):61-64 [12] Toda N. On the growth of meromorphic solutions of some higher order differential equations. J Math Soc, Japan, 1986, 38(3):439-451 [13] Tu Z H, Xiao X Z. On the meromorphic solutions of system of higher order algebraic differential equations. Complex Variables, 1990, 15(3):197-209 [14] Ablowitz M J, Halburd R, Herbst B. On the extension of the Painleve property to difference equations. Nonlinearity, 2000, 13(3):889-905 [15] Chen Z X. On difference equations relating to Gamma function. Acta Mathematica Scientia, 2011, 31B(4):1281-1294 [16] Chiang Y M, Feng S J. On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane. Ramanujan Journal, 2008, 16(1):105-129 [17] Gao L Y. On meromorphic solutions of a type of difference equations. Chinese Ann Math, 2014, 35A(2):193-202 [18] Goldstein R. Some results on factorisation of meromorphic functions. J London Math Soc, 1971, 4(4):357-364 [19] Goldstein R. On meromorphic solutions of certain functional equations. Aequationes Math, 197818(1/2):112-157 [20] Halburd R G, Korhonen R J. Difference analogue of the lemma on the logarithmic derivative with applications to difference equations. Journal of Mathematical Analysis and Applications, 2006, 314(2):477-487 [21] Heittokangas J, Korhonen, R, Laine I, Rirppo J, Tohge K. Complex difference equations of Malmquist type. Computational Methods and Theory, 2001, 1(1):27-39 [22] Huang Z B, Chen Z X. Meromorphic solutions of some complex difference equations. Advances in difference equations, 2009, Article ID 982681, 10 pages [23] Korhonen R. A new Clunie type theorem for difference polynomials. Difference Equ Appl, 2011, 17(3):387-400 [24] Laine I, Rieppo J, Silvennoinen H. Remarks on complex difference equations. Computational Methods and Function Theory, 2005, 5(1):77-88 [25] Mohon'ko A Z. The Nevanlinna characteristics of certain meromorphic functions. Teor Funktsional Anal I Prilozhen, 1971, 14(14):83-87(in Russian) [26] Weissenborn G. On the theorem of Tumura and Clunie. Bull London Math Soc, 1986, 18(4):371-373 [27] Zhang X, Liao L W. Meromorphic solutions of complex difference and differential equations and their properties. Nanjing:Nanjing University, 2014 [28] Gao L Y. Systems of complex difference equations of Malmquist type. Acta Mathematica Sinica, 2012, 55(2):293-300 [29] Li H C. On existence of solutions of differential-difference equations. Math Meth Appl Sci, 2016, 39(1):144-151 |
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