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 $$af^2(z)+2\omega f(z)(a_0f(z)+L^{k+s}_{1,2}(f(z)))+b(a_0f(z)+L^{k+s}_{1,2}(f(z)))^2=e^{g(z)}$$
by utilizing Nevanlinna’s theory in several complex variables, where $g(z)$ is entire
functions in $\mathbb{C}^n,$ $ω\ne 0$ and $a, b, ω ∈ \mathbb{C}.$ 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.