Acknowledgement
The authors would like to thank the referees for their thorough comments and helpful suggestions.
References
- G. E. Andrews, R. A. Askey, and R. Roy, Special functions, Encyclopedia of Mathematics and its Applications, 71, Cambridge Univ. Press, Cambridge, 1999. https://doi.org/10.1017/CBO9781107325937
- D. C. Barnett, R. G. Halburd, W. Morgan, and R. J. Korhonen, Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 3, 457-474. https://doi.org/10.1017/S0308210506000102
- M. F. Chen, Y. Y. Jiang, and Z. S. Gao, Growth of meromorphic solutions of certain types of q-difference differential equations, Adv. Difference Equ. 2017 (2017), Paper No. 37, 16 pp. https://doi.org/10.1186/s13662-017-1072-y
- L. Y. Gao, On m-admissible components of solution, Complex Variables Theory Appl. 35 (1998), no. 4, 297-306. https://doi.org/10.1080/17476939808815088
- W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
- Y. Z. He and X. Z. Xiao, Algebroid Functions and Ordinary Differential Equations, Science Press, Beijing 1988.
- P.-C. Hu and M. L. Liu, A Malmquist type theorem for a class of delay differential equations, Bull. Malays. Math. Sci. Soc. 44 (2021), no. 1, 131-145. https://doi.org/10.1007/s40840-020-00941-8
- P.-C. Hu, W. Wang, and L. Wu, Entire solutions of differential-difference equations of Fermat type, Bull. Korean Math. Soc. 59 (2022), no. 1, 83-99. https://doi.org/10.4134/BKMS.b210099
- Z. B. Huang, Value distribution and uniqueness on q-differences of meromorphic functions, Bull. Korean Math. Soc. 50 (2013), no. 4, 1157-1171. https://doi.org/10.4134/BKMS.2013.50.4.1157
- I. Laine, Nevanlinna theory and complex differential equations, De Gruyter Studies in Mathematics, 15, de Gruyter, Berlin, 1993. https://doi.org/10.1515/9783110863147
- I. Laine and Z. Latreuch, Remarks on meromorphic solutions of some delay-differential equations, Anal. Math. 48 (2022), no. 4, 1081-1104. https://doi.org/10.1007/s10476-022-0172-4
- I. Laine and C.-C. Yang, Clunie theorems for difference and q-difference polynomials, J. Lond. Math. Soc. (2) 76 (2007), no. 3, 556-566. https://doi.org/10.1112/jlms/jdm073
- A. Z. Mokhon'ko and V. D. Mokhon'ko, Estimates for the Nevanlinna characteristics of some classes of meromorphic functions and their applications to differential equations, Sib. Math. J. 15 (1974), no. 6, 921-934. https://doi.org/10.1007/BF00966560
- Z. H. Tu and X. Z. Xiao, On the meromorphic solutions of system of higher-order algebraic differential equations, Complex Variables Theory Appl. 15 (1990), no. 3, 197-209. https://doi.org/10.1080/17476939008814451
- Y. Wang, Solutions of complex difference and q-difference equations, Adv. Difference Equ. 2016 (2016), no. 1, 1-22. https://doi.org/10.1186/s13662-016-0790-x
- X. L. Wang, H. Wang, and H. Y. Xu, The existence of solutions of q-difference differential equations, SpringerPlus. 5 (2016), no. 1, 1-9. https://doi.org/10.1186/s40064-016-2179-4
- L. Xu and T.-B. Cao, Meromorphic solutions of delay differential equations related to logistic type and generalizations, Bull. Sci. Math. 172 (2021), Paper No. 103040, 25 pp. https://doi.org/10.1016/j.bulsci.2021.103040
- J. F. Xu and L. Luo, Some q-shift difference results on Hayman conjecture and uniqueness theorems, Bull. Iranian Math. Soc. 48 (2022), no. 3, 1193-1204. https://doi.org/10.1007/s41980-021-00574-y
- H. Y. Xu, L. Yang, and H. Wang, Growth of the solutions of some q-difference differential equations, Adv. Difference Equ. 2015 (2015), 172, 12 pp.
- C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing/New York, 2003.
- J. Zhang and R. Korhonen, On the Nevanlinna characteristic of f(qz) and its applications, J. Math. Anal. Appl. 369 (2010), no. 2, 537-544. https://doi.org/10.1016/j.jmaa.2010.03.038
- X.-M. Zheng and Z. X. Chen, Some properties of meromorphic solutions of q-difference equations, J. Math. Anal. Appl. 361 (2010), no. 2, 472-480. https://doi.org/10.1016/j.jmaa.2009.07.009