Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 73, pp. 1-9.
Title: Entire solutions for a nonlinear differential equation
Authors: Jianming Qi (Shanghai Dianji Univ., China)
Jie Ding (Shandong Univ., Jinan, China)
Taiying Zhu (Shanghai Dianji Univ., China)
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.