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April 2020 Meromorphic solutions of two certain types of nonlinear differential equations
Wei Chen, Qiong Wang, Wenjun Yuan
Rocky Mountain J. Math. 50(2): 479-497 (April 2020). DOI: 10.1216/rmj.2020.50.479

## Abstract

We investigate the meromorphic solutions of two types of nonlinear differential equations of the form

$\begin{array}{lllllll}\hfill b{f}^{n}+a{f}^{n-1}{f}^{\prime }+{Q}_{d}\left(f\right)& =u\left(z\right){e}^{v\left(z\right)},\phantom{\rule{2em}{0ex}}& \hfill n\ge d+2,& \phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}& \hfill \\ \hfill {f}^{n}+{f}^{n-1}{f}^{\prime }+{Q}_{d}\left(f\right)& ={P}_{1}\left(z\right){e}^{{\alpha }_{1}}+{P}_{2}\left(z\right){e}^{{\alpha }_{2}},\phantom{\rule{2em}{0ex}}& \hfill n\ge d+3,& \phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}& \hfill \end{array}$

where $a,b$ are constants with $\left(a,b\right)\ne \left(0,0\right)$ and $n,d$ are positive integers, $u,{P}_{1},{P}_{2}$ are nonzero rational functions, $v,{\alpha }_{1},{\alpha }_{2}$ are nonconstant polynomials, and ${Q}_{d}\left(f\right)$ denotes a differential polynomial in $f$ with rational functions as its coefficients. Our results improve some recent related results.

## Citation

Wei Chen. Qiong Wang. Wenjun Yuan. "Meromorphic solutions of two certain types of nonlinear differential equations." Rocky Mountain J. Math. 50 (2) 479 - 497, April 2020. https://doi.org/10.1216/rmj.2020.50.479

## Information

Received: 19 June 2019; Revised: 28 October 2019; Accepted: 28 October 2019; Published: April 2020
First available in Project Euclid: 29 May 2020

zbMATH: 07210973
MathSciNet: MR4104388
Digital Object Identifier: 10.1216/rmj.2020.50.479

Subjects:
Primary: 30D30, 30D35, 33E30