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In this paper, the expressions of meromorphic solutions of the following nonlinear complex differential equation of the form $$f^{n}+Q_{d}(z,f)=\sum_{i=1}^{3}p_{i}(z)e^{\alpha_{i}(z)}$$ are studied by using Nevanlinna theory, where $n\geq5$ is an integer, $Q_{d}(z,f)$ is a differential polynomial in $f$ of degree $d\leq n-4$~with rational functions as its coefficients, $p_{1}(z)$, $p_{2}(z)$, $p_{3}(z)$~are non-vanishing rational functions, and $\alpha_{1}(z)$, $\alpha_{2}(z)$, $\alpha_{3}(z)$ are nonconstant polynomials such that $\alpha_{1}'(z)$, $\alpha_{2}'(z)$, $\alpha_{3}'(z)$ are distinct each other. Moreover, examples are given to illustrate the accuracy of the condition.
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참고문헌 (20)
참고문헌 신청
M. F. Chen / 2018 / Entire solutions of certain type of nonlinear differential equations and differential-difference equations / J. Comput. Anal. Appl 24(1):137~147
J. Clunie / 1962 / On integral and meromorphic functions / J. London Math. Soc 37:17~27
Xianjing Dong / 2019 / Meromorphic solutions of certain type of differential-difference equations / Journal of Mathematical Analysis and Applications 470(1):327~339
R. Halburd / 2017 / Growth of meromorphic solutions of delay differential equations / Proc. Amer. Math. Soc 145(6):2513~2526
W. K. Hayman / 1964 / Meromorphic Functions, Oxford Mathematical Monographs / Clarendon Press
J. Clunie / 1962 / On integral and meromorphic functions / J. London Math. Soc 37:17~27
Xianjing Dong / 2019 / Meromorphic solutions of certain type of differential-difference equations / Journal of Mathematical Analysis and Applications 470(1):327~339
R. Halburd / 2017 / Growth of meromorphic solutions of delay differential equations / Proc. Amer. Math. Soc 145(6):2513~2526
W. K. Hayman / 1964 / Meromorphic Functions, Oxford Mathematical Monographs / Clarendon Press
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