Acknowledgement
The authors would like to thank the referee for his/her thorough review with constructive suggestions and valuable comments on the paper, especially the construction of h(z) in formula (54) which plays an important role in the proof of Theorem 1.3 Case 1.
References
- Z. X. Chen, Complex Differences and Difference Equations, Science Press, 2014.
- M. F. Chen and Z. S. Gao, Entire solutions of certain type of nonlinear differential equations and differential-difference equations, J. Comput. Anal. Appl. 24 (2018), no. 1, 137-147.
- J. B. Conway, Functions of One Complex Variable. II, Graduate Texts in Mathematics, 159, Springer-Verlag, New York, 1995. https://doi.org/10.1007/978-1-4612-0817-4
- W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
- X. H. Hua, Some extensions of the Tumura-Clunie theorem, Complex Variables Theory Appl. 16 (1991), no. 1, 69-77. https://doi.org/10.1080/17476938208814467
- I. Laine, Nevanlinna theory and complex differential equations, De Gruyter Studies in Mathematics, 15, Walter de Gruyter & Co., Berlin, 1993. https://doi.org/10.1515/9783110863147
- P. Li, Entire solutions of certain type of differential equations II, J. Math. Anal. Appl. 375 (2011), no. 1, 310-319. https://doi.org/10.1016/j.jmaa.2010.09.026
- N. Li and L. Z. Yang, Some results on meromorphic solutions of certain nonlinear differential equations, Bull. Korean Math. Soc. accepted, https://doi.org/10.4134/BKMS.b190535
- L.-W. Liao, Non-linear differential equations and Hayman's theorem on differential polynomials, Complex Var. Elliptic Equ. 60 (2015), no. 6, 748-756. https://doi.org/10.1080/17476933.2014.972390
- L.-W. Liao, C.-C. Yang, and J.-J. Zhang, On meromorphic solutions of certain type of non-linear differential equations, Ann. Acad. Sci. Fenn. Math. 38 (2013), no. 2, 581-593. https://doi.org/10.5186/aasfm.2013.3840
- J. X. Rong and J. F. Xu, Three results on the nonlinear differential equations and differential-difference equations, Mathematics 7 (2019), no. 6, 539. https://doi.org/10.3390/math7060539
- C.-C. Yang and H.-X. Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557, Kluwer Academic Publishers Group, Dordrecht, 2003.
- J. Zhang and L. Liao, A note on Malmquist-Yosida type theorem of higher order algebraic differential equations, Acta Math. Sci. Ser. B (Engl. Ed.) 38 (2018), no. 2, 471-478. https://doi.org/10.1016/S0252-9602(18)30761-6