Three Results on the Nonlinear Differential Equations and Differential-Difference Equations

Mathematics

Junfeng Xu¹  Jianxun Rong¹ 

[1] School of Mathematics and Computational Science, Wuyi University, Jiangmen 529020, China;

关键词: entire solution;    Nevanlinna theory;    difference equation;    differential-difference equation;   

DOI  :  10.3390/math7060539

来源: DOAJ

【 摘 要 】

We mainly study the transcendental entire solutions of the differential equation $f^n(z)+P(f)=p_1{e}^{{\alpha }_{1}z}+p_2{e}^{{\alpha }_{2}z}$ , where $p_1$ , $p_2$ , ${\alpha }_1$ and ${\alpha }_2$ are nonzero constants satisfying ${\alpha }_1\ne {\alpha }_2$ and $P(f)$ is a differential polynomial in f of degree $n-1$ . We improve Chen and Gao’s results and partially answer a question proposed by Li (J. Math. Anal. Appl. 375 (2011), pp. 310−319).

【 授权许可】

Unknown