Entire solutions for a nonlinear differential equation

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 $ngeq 2$ 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].

Keywords

• Transcendental entire functions
• Nevanlinna theory
• differential equations