## 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 deg_{w}*(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