Study on the existence of solutions to two specific types of differential-difference equations. (English) Zbl 1417.34203
Summary: 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.
MSC:
| 34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
| 30D35 | Value distribution of meromorphic functions of one complex variable, Nevanlinna theory |
| 34M05 | Entire and meromorphic solutions to ordinary differential equations in the complex domain |
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