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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  