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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.9
- 수록면
- 975 - 995 (21page)
- DOI
- 10.4134/JKMS.j230387
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초록· 키워드
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In this paper, we utilize Nevanlinna theory to study the existence and forms of solutions for quadratic trinomial complex partial differential-difference equations of the form $ aF^2+2\omega FG+bG^2=\exp(g) $, where $ ab\neq 0, \omega\in\mathbb{C} $ with $ \omega^2\neq 0, ab $ and $g$ is a polynomial in $\mathbb{C}^n$. In order to achieve a comprehensive and thorough analysis, we study the characteristics of solutions in two specific cases: one when $ \omega^2\neq 0, ab $ and the other when $ \omega=0 $. Because polynomials in several complex variables may exhibit periodic behavior, a property that differs from polynomials in single complex variables, our study of finding solutions of equations in $\mathbb{C}^n$ is significant. The main results of the paper improved several known results in $\mathbb{C}^n$ for $n\geq 2$. Additionally, the corollaries generalize results of Xu \emph{et al.} [Rocky Mountain J. Math. \textbf{52}(6) (2022), 2169--2187] for trinomial equations with arbitrary coefficients in $\mathbb{C}^n$. Finally, we provide examples that endorse the validity of the conclusions drawn from the main results and their related remarks.
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