Electron. J. Diff. Equ., Vol. 2015 (2015), No. 22, pp. 1-8.

Entire solutions for nonlinear differential-difference equations

Na Xu, Ting-Bin Cao, Kai Liu

Abstract:
In this article, we study entire solutions of the nonlinear differential-difference equation
$$ q(z)f^{n}(z)+a(z)f^{(k)}(z+1)=p_1(z)e^{q_1(z)}+p_2(z)e^{q_2(z)} $$
where $p_1(z)$, $p_2(z)$ are nonzero polynomials, $q_1(z)$, $q_2(z)$ are nonconstant polynomials, $q(z)$, $a(z)$ are nonzero entire functions of finite order, $n\geq2$ is an integer. We obtain additional results for case: $n=3$, $q_1(z)=-q_2(z)$, and $p_1(z)$, $p_2(z)$ nonzero constants.

Submitted July 15, 2014. Published January 27, 2015.
Math Subject Classifications: 30D35, 39A05.
Key Words: Nevanlinna theory; differential-difference equation; entire function.

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Na Xu
School of Mathematical Sciences, Xiamen University
Xiamen 361005, China
email: xuna406@163.com
Ting-Bin Cao
Department of Mathematics, Nanchang University
Nanchang, Jiangxi 330031, China
email: tbcao@ncu.edu.cn
Kai Liu
Department of Mathematics, Nanchang University
Nanchang, Jiangxi 330031, China
email: liukai418@126.com

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