Geodesic
Entire solutions for a nonlinear differential equation
Electronic Journal of Differential Equations, Tome 2011 (2011).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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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/