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Entire solutions for some Fermat type functional equations concerning difference and partial differential in ℂ2

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Abstract

The main purpose of this paper is concerned with the existence and the forms of transcendental entire solutions of several Fermat type functional equations concerning difference and partial differential in ℂ2, by utilizing the Nevanlinna theory of meromorphic functions in several complex variables. Some results are obtained to give the forms of entire solutions for such equations, which are some improvements and generalizations of the previous theorems given by Xu and Cao, Liu and Dong. Moreover, some examples are given to show that there are great differences in the forms of transcendental entire solutions with finite order of Fermat type functional equations between in several complex variables and in a single complex variable.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, Jiangxi, 330022, P. R. China

    X.-M. Zheng

  2. School of Mathematics and Computer Science, Shangrao Normal University, Shangrao, Jiangxi, 334001, P. R. China

    H.-Y. Xu

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  1. X.-M. Zheng
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  2. H.-Y. Xu
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Correspondence to H.-Y. Xu.

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Supported by the National Natural Science Foundation of China (Nos. 11761035, 12161074) and the Natural Science Foundation of Jiangxi Province in China (No. 20181BAB201001).

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Zheng, XM., Xu, HY. Entire solutions for some Fermat type functional equations concerning difference and partial differential in ℂ2. Anal Math 48, 199–226 (2022). https://doi.org/10.1007/s10476-021-0113-7

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  • DOI: https://doi.org/10.1007/s10476-021-0113-7

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