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On Entire Solutions of Some Differential-Difference Equations

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Abstract

In this paper, we will investigate the properties of entire solutions with finite order of the Fermat type difference or differential-difference equations. This is continuation of a recent paper (Liu et al. in Arch. Math. 99, 147–155, 2012). In addition, we also consider the value distribution and growth of the entire solutions of linear differential-difference equation \(f^{(k)}(z)=h(z)f(z+c),\) where \(h(z)\) is a non-zero meromorphic function, \(c\) is a non-zero constant. Our results partially answer the question given in Liu et al. (Arch. Math. 99, 147–155, 2012).

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Acknowledgments

The authors thank the referee for some helpful suggestions to improve the readability of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Jiangxi, 330031, Nanchang, People’s Republic of China

    Kai Liu

  2. School of Mathematics, Shandong University, Jinan, 250100, Shandong, People’s Republic of China

    Lianzhong Yang

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  1. Kai Liu
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  2. Lianzhong Yang
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Correspondence to Kai Liu.

Additional information

Communicated by Ilpo Laine.

This work was partially supported by the NSFC (No. 11301260, 11101201, 11171013), the NSF of Shandong (No. ZR2010AM030), the NSF of Jiangxi (No. 20132BAB211003) and the YFED of Jiangxi (No. GJJ13078) of China.

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Liu, K., Yang, L. On Entire Solutions of Some Differential-Difference Equations. Comput. Methods Funct. Theory 13, 433–447 (2013). https://doi.org/10.1007/s40315-013-0030-2

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