TY - JOUR
T1 - On Solutions of Differential-Difference Equations in $\mathbb{C}^n$
AU - Yang , Ling
AU - Chen , Lu
AU - Zhang , Shimei
JO - Analysis in Theory and Applications
VL - 1
SP - 52
EP - 79
PY - 2025
DA - 2025/04
SN - 41
DO - http://doi.org/10.4208/ata.OA-2024-0044
UR - https://global-sci.org/intro/article_detail/ata/23958.html
KW - Differential-difference equations, Nevanlinna theory, finite order, entire solutions.
AB - <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>