Characterizations of entire solutions for the system of Fermat-type binomial and trinomial shift equations in ℂn#

• Autorzy: Haldar Goutam , Banerjee Abhijit

Identyfikatory

DOI

10.1515/dema-2023-0104

• Języki publikacji: EN

Abstrakty

EN

In this article, we investigate the existence and the precise form of finite-order transcendental entire solutions of some system of Fermat-type quadratic binomial and trinomial shift equations in ℂn . Our results are the generalizations of the results of [H. Y. Xu, S. Y. Liu, and Q. P. Li, Entire solutions for several systems of nonlinear difference and partial differential-difference equations of Fermat-type, J. Math. Anal. Appl. 483 (2020), 123641, 1–22, DOI: https://doi.org/10.1016/j.jmaa.2019.123641.] and [H. Y. Xu and Y. Y. Jiang, Results on entire and meromorphic solutions for several systems of quadratic trinomial functional equations with two complex variables, RACSAM 116 (2022), 8, DOI: https://doi.org/10.1007/s13398-021-01154-9.] .] to a large extent. Most interestingly, as a consequence of our main result, we have shown that the system of quadratic trinomial shift equation has no solution when it reduces to a system of quadratic trinomial difference equation. In addition, some examples relevant to the content of the article have been exhibited.

Słowa kluczowe

EN

functions of several complex variables; Fermat-type shift equations; entire solutions; Nevanlinna theory

PL

funkcje wielu zmiennych zespolonych; rozwiązania całkowite; teoria Nevanlinny

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20230104
• Opis fizyczny: Bibliogr. 41 poz.

Twórcy

autor

Haldar Goutam

• Department of Mathematics, Malda College - 732101, West Bengal, India
• Ghani Khan Choudhury Institute of Engineering and Technology, Narayanpur, Malda 732141, West Bengal, India

autor

Banerjee Abhijit

• Department of Mathematics, University of Kalyani, West Bengal 741235, India

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).