Study on the existence of solutions to two specific types of differential-difference equations

Authors: QIONG WANG, QIONGYAN WANG

Abstract: This paper concerns the description of the entire or meromorphic solutions to two certain types of differential-difference equations under some certain conditions. The significance of our results lies in that we find the entire solutions of the second type equation with the form $f=Ae^{Bz}$, where $A,B$ are constants that are completely determined only by coefficients and correlated indices. Our results are accurate in a certain sense and are supplemented by an example. In particular, our results generalize and improve a result of Zhang and Huang, and they are closely related to recent results by Dong and Liao.

Keywords: Differential-difference equations, hyperorder, meromorphic solutions, Nevanlinna theory

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