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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회보 대한수학회보 제59권 제5호
- 발행연도
- 2022.9
- 수록면
- 1,145 - 1,166 (22page)
- DOI
- 10.4134/BKMS.b210637
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초록· 키워드
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In this paper, for a transcendental meromorphic function $f$ and $a\in \mathbb{C}$, we have exhaustively studied the nature and form of solutions of a new type of non-linear differential equation of the following form which has never been investigated earlier: \[f^n+af^{n-2}f'+ P_d(z,f) = \sum_{i=1}^{k}p_i(z)e^{\alpha_i(z)}, \] where $P_d(z,f)$ is a differential polynomial of $f$, $p_i$'s and $\alpha_{i}$'s are non-vanishing rational functions and non-constant polynomials, respectively. When $a=0$, we have pointed out a major lacuna in a recent result of Xue \cite{xue_math slovaca20} and rectifying the result, presented the corrected form of the same equation at a large extent. In addition, our main result is also an improvement of a recent result of Chen-Lian \cite{chen lian_BKMS20} by rectifying a gap in the proof of the theorem of the same paper. The case $a\neq 0$ has also been manipulated to determine the form of the solutions. We also illustrate a handful number of examples for showing the accuracy of our results.
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