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Entire solutions of Fermat type differential-difference equations

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Abstract

We mainly discuss entire solutions with finite order of the following Fermat type differential-difference equations

$$\begin{array}{ll}(f)^{n}+f(z+c)^{m}=1;\\f^{\prime}(z)^{n}+f(z+c)^{m}=1;\\ f^{\prime}(z)^{n}+[f(z+c)-f(z)]^{m}=1,\end{array}$$

where m, n are positive integers.

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Authors and Affiliations

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

    Kai Liu, Tingbin Cao & Hongzhe Cao

Authors
  1. Kai Liu
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  2. Tingbin Cao
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  3. Hongzhe Cao
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Corresponding author

Correspondence to Kai Liu.

Additional information

This work was partially supported by the NSFC (No. 11026110, 11101201), the NSF of Jiangxi (No. 2010GQS0144, 2010GQS0139).

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Liu, K., Cao, T. & Cao, H. Entire solutions of Fermat type differential-difference equations. Arch. Math. 99, 147–155 (2012). https://doi.org/10.1007/s00013-012-0408-9

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  • DOI: https://doi.org/10.1007/s00013-012-0408-9

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