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Results on entire and meromorphic solutions for several systems of quadratic trinomial functional equations with two complex variables

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Abstract

In this paper, we establish several theorems about the existence and the forms of entire solutions with finite order for some systems of quadratic trinomial functional equations with two complex variables, which are some improvements and generalizations of the previous theorems given by Xu and Cao, Xu, Liu and Li. Moreover, some examples are given show that there are significant differences in the forms of transcendental entire solutions with finite order of some systems of functional equations with complex between two variables and a single variable.

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Data Availability Statement

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Acknowledgements

We gratefully appreciate Professor Risto Korhonen for reading the manuscript very carefully and making a number of valuable and kind comments which improved the presentation.

Funding

This work was supported by the National Natural Science Foundation of China 12161074, the Natural Science Foundation of Jiangxi Province in China 20181BAB201001, and the Foundation of Education Department of Jiangxi (GJJ190876, GJJ202303, GJJ201813, GJJ191042) of China.

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Authors and Affiliations

  1. Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou, Jiangxi, 341000, China

    Hong Yan Xu

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

    Hong Yan Xu

  3. School of Mathematics and Computer, Jiangxi Science and Technology Normal University, Nanchang, Jiangxi, 330038, China

    Ye Yang Jiang

  4. Department of Physics and mathematics, University of Eastern Finland, P. O. Box 111, Fl-80101, Joensuu, Finland

    Ye Yang Jiang

Authors
  1. Hong Yan Xu
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  2. Ye Yang Jiang
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Contributions

HYX completed the main part of this article, HYX and YYJ corrected the main theorems. All authors gave final approval for publication.

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Correspondence to Hong Yan Xu.

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Xu, H.Y., Jiang, Y.Y. Results on entire and meromorphic solutions for several systems of quadratic trinomial functional equations with two complex variables. RACSAM 116, 8 (2022). https://doi.org/10.1007/s13398-021-01154-9

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  • DOI: https://doi.org/10.1007/s13398-021-01154-9

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