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On entire solutions of Fermat type difference and kth order partial differential difference equations in several complex variables

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Abstract

In this paper, we investigate the existence and specific form of finite order transcendental entire solutions of certain equations including a Fermat-type functional first-order linear difference equation in \(\mathbb {C}^n\), \(n\geqslant 2\) and a kth order partial differential difference equation in \(\mathbb {C}^2\). The paper builds upon the previous works of Xu and Cao (Mediterr J Math 15:1–14, 2018; Mediterr J Math 17:1–4, 2020) and Haldar (Mediterr J Math 20: 50, 2023) whose results are extended and further developed in this study. We exhibit several examples to demonstrate the precision and applicability of our results to illustrate how our findings can be utilized in different scenarios or problem contexts. Towards the end of the paper, in the last section, we discuss some relevant questions that have emerged from one of the examples in the paper which also suggest potential directions for further research.

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Acknowledgements

The authors would like to thank the anonymous referee(s) for the helpful suggestions and comments to improve the clarity and presentation of the paper.

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  1. Goutam Haldar

    Present address: Ghani Khan Choudhury Institute of Engineering and Technology, Narayanpur, Malda, 732141, West Bengal, India

Authors and Affiliations

  1. Department of Mathematics, Malda College, Malda, West Bengal, 732101, India

    Goutam Haldar

  2. Department of Mathematics, University of Kalyani, Kalyani, West Bengal, 741235, India

    Abhijit Banerjee

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  1. Goutam Haldar
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Correspondence to Goutam Haldar.

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Haldar, G., Banerjee, A. On entire solutions of Fermat type difference and kth order partial differential difference equations in several complex variables. Afr. Mat. 35, 45 (2024). https://doi.org/10.1007/s13370-024-01188-3

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