@Article{ATA-41-52,
author = {Yang , LingChen , Lu and Zhang , Shimei},
title = {On Solutions of Differential-Difference Equations in $\mathbb{C}^n$},
journal = {Analysis in Theory and Applications},
year = {2025},
volume = {41},
number = {1},
pages = {52--79},
abstract = {<p style="text-align: justify;">In this paper, we mainly explore the existence of entire solutions of the
quadratic trinomial partial differential-difference equation $$af^2(z)+2\omega f(z)(a_0f(z)+L^{k+s}_{1,2}(f(z)))+b(a_0f(z)+L^{k+s}_{1,2}(f(z)))^2=e^{g(z)}$$<br/>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.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-2024-0044},
url = {http://global-sci.org/intro/article_detail/ata/23958.html}
}