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Meromorphic solutions of three certain types of non-linear difference equations
Author(s) -
Min Feng Chen,
Zhi Bo Huang,
Zong Sheng Gao
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021680
Subject(s) - mathematics , combinatorics , polynomial , mathematical analysis
In this paper, the representations of meromorphic solutions for three types of non-linear difference equations of form \begin{document}$ f^{n}(z)+P_{d}(z, f) = u(z)e^{v(z)}, $\end{document} \begin{document}$ f^{n}(z)+P_{d}(z, f) = p_{1}e^{\lambda z}+p_{2}e^{-\lambda z} $\end{document} and \begin{document}$ f^{n}(z)+P_{d}(z, f) = p_{1}e^{\alpha_{1}z}+p_{2}e^{\alpha_{2}z} $\end{document} are investigated, where $ n\geq 2 $ is an integer, $ P_{d}(z, f) $ is a difference polynomial in $ f $ of degree $ d\leq n-1 $ with small coefficients, $ u(z) $ is a non-zero polynomial, $ v(z) $ is a non-constant polynomial, $ \lambda, p_{j}, \alpha_{j}\; (j = 1, 2) $ are non-zero constants. Some examples are also presented to show our results are best in certain sense.

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