Electron. J. Diff. Equ., Vol. 2011 (2011), No. 73, pp. 1-9.

Entire solutions for a nonlinear differential equation

Jianming Qi, Jie Ding, Taiying Zhu

Abstract:
In this article, we study the existence of solutions to the differential equation
$$ f^n(z)+P(f)= P_1e^{h_1}+ P_2e^{h_2}, $$
where $n\geq 2$ is an positive integer, f is a transcendental entire function, $P(f)$ is a differential polynomial in f of degree less than or equal n-1, $P_1, P_2$ are small functions of $e^z$, $h_1$, $h_2$ are polynomials, and $z$ is in the open complex plane $\mathbb{C}$. Our results extend those obtained by Li [6,7,8].

Submitted July 10, 2010. Published June 15, 2011.
Math Subject Classifications: 30D35, 30D45.
Key Words: Transcendental entire functions; Nevanlinna theory; differential equations.

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Jianming Qi
Department of Mathematics and Physics
Shanghai Dianji University
Shanghai 200240, China
email: qijianming1981@gmail.com
Jie Ding
Department of Mathematics, Shandong University
Jinan 250100, China
email: dingjie169@163.com
Taiying Zhu
Department of Mathematics and Physics
Shanghai Dianji University
Shanghai 200240, China
email: ztyyyy@163.com

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