Abstract
We obtain necessary conditions for the non-linear complex differential-difference equations
to admit transcendental meromorphic solutions w(z) such that ρ2(w) < 1, where R(z,w(z)) is rational in w(z) with rational coefficients, a(z) is a rational function and ρ2(w) is the hyper-order of w(z). Our results can be seen as the product versions on an equation of another type investigated by Halburd and Korhonen [3]. We also provide an idea which implies that the case of degw(R(z,w)) = 4 in the original proof of [3, Theorem 1.1] can be organized in a short way.
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Acknowledgement
The authors would like to thank Professor Risto Korhonen and the reviewer for their helpful suggestions and comments for the paper.
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This work was partially supported by the NSFC (No. 11661052), the fund of Jiangxi Province for Outstanding Youth (No. 20171BCB23003) and the NSF of Jiangxi (No. 20161BAB211005).
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Liu, K., Song, C.J. Non-Linear Complex Differentialdifference Equations Admit Meromorphic Solutions. Anal Math 45, 569–582 (2019). https://doi.org/10.1007/s10476-019-0990-1
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DOI: https://doi.org/10.1007/s10476-019-0990-1