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On Solutions of Differential-Difference Equations in Cn

On Solutions of Differential-Difference Equations in $\mathbb{C}^n$

Year:    2025

Author:    Ling Yang, Lu Chen, Shimei Zhang

Analysis in Theory and Applications, Vol. 41 (2025), Iss. 1 : pp. 52–79

Abstract

In this paper, we mainly explore the existence of entire solutions of the quadratic trinomial partial differential-difference equation af2(z)+2ωf(z)(a0f(z)+Lk+s1,2(f(z)))+b(a0f(z)+Lk+s1,2(f(z)))2=eg(z)
by utilizing Nevanlinna’s theory in several complex variables, where g(z) is entire functions in Cn, ω0 and a,b,ωC. Furthermore, we get the exact froms of solutions of the above differential-difference equation when ω=0. Our results are generalizations of previous results. In addition, some examples are given to illustrate the accuracy of the results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.OA-2024-0044

Analysis in Theory and Applications, Vol. 41 (2025), Iss. 1 : pp. 52–79

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords:    Differential-difference equations Nevanlinna theory finite order entire solutions.

Author Details

Ling Yang Email

Lu Chen Email

Shimei Zhang Email