On Solutions of Differential-Difference Equations in $\mathbb{C}^n$
Year: 2025
Type: article
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.
Authors: Ling Yang, Lu Chen, Shimei Zhang
Institution: Guizhou Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409307101