Geodesic
Entire solutions for a nonlinear differential equation
Electronic journal of differential equations, Tome 2011 (2011)
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].
Classification : 30D35, 30D45
Keywords: transcendental entire functions, Nevanlinna theory, differential equations 
@article{EJDE_2011__2011__a2,
     author = {Qi,  Jianming and Ding,  Jie and Zhu,  Taiying},
     title = {Entire solutions for a nonlinear differential equation},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1226.30034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a2/}
}
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Qi,  Jianming; Ding,  Jie; Zhu,  Taiying. Entire solutions for a nonlinear differential equation. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a2/