This paper is to study the unicity of transcendental meromorphic solutions to some nonlinear difference equations. Let be a nonzero rational function. Consider the uniqueness of transcendental meromorphic solutions to some nonlinear difference equations of the form . For two finite order transcendental meromorphic solutions of the equation above, it shows that they are almost equal to each other except for a nonconstant factor, if they have the same zeros and poles counting multiplicities, when . Two relative results are proved, and examples to show sharpness of our results are provided.
References
[1]
Laine, I. (1993) Nevanlinna Theory and Complex Differential Equations. In: de Gruyter Studies in Mathematics, Walter de Gruyter, Berlin, New York.
[2]
Yang, C.C. and Yi, H.X. (2003) Uniqueness Theory of Meromorphic Functions. Kluwer Academic Publishers, Dordrecht.
[3]
Ronkainen, O. (2010) Meromorphic Solutions of Difference Painlevé Equations. Annales Academiae Scientiarum Fennicae Mathematica, 155, 1-59.
Cui, N. and Chen, Z.X. (2017) Uniqueness for Meromorphic Solutions Sharing Three Values with a Meromorphic Function to Some Linear Difference Equations. Chinese Annals of Mathematics, Series A, 38, 13-22.
[6]
Lü, F., Han, Q. and Lü, W.R. (2016) On Unicity of Meromorphic Solutions to Difference Equations of Malmquist Type. Bulletin of the Australian Mathematical Society, 93, 92-98. https://doi.org/10.1017/S0004972715000787
[7]
Zhang, J.L. and Yang, L.Z. (2014) Meromorphic Solutions of Painlevé III Difference Equations. Acta Mathematica Sinica, 57, 181-188.
[8]
Lan, S.T. and Chen, Z.X. (2014) On Properties of Meromorphic Solutions of Certain Difference Painlevé Equations. Abstract and Applied Analysis, 2014, Article ID: 208701. https://doi.org/10.1155/2014/208701
![\"\"](\"Edit_a93a5d6e-8784-42a3-8505-63a411df431f.bmp\")
be a nonzero rational function. Consider the uniqueness of transcendental meromorphic solutions to some nonlinear difference equations of the form ![\"\"](\"Edit_9a3b22ca-428e-4b98-833c-60346c21287c.bmp\")
. For two finite order transcendental meromorphic solutions of the equation above, it shows that they are almost equal to each other except for a nonconstant factor, if they have the same zeros and poles counting multiplicities, when ![\"\"](\"Edit_dcbaa877-ba9f-44df-9033-6b1e818ac8cc.bmp\")
. Two relative results are proved, and examples to show sharpness of our results are provided.
