In this paper, we are mainly concerned with one certain type of non-linear complex differential equation $f^n(z)+P_d(z,f)=p_1{e}^{{\alpha }_{1}z}+p_2{e}^{{\alpha }_{2}z},$ where $p_1,p_2,{\alpha }_1,{\alpha }_2$ are non-zero constants and $P_d(z,f)$ is a differential polynomial in f of degree d at most n−1. For this kind of equation, if it admits a meromorphic solution such that $N(r,f)=S(r,f)$, then firstly we give a positive answer to Li's question with a weaker restriction on ${\alpha }_1$ and ${\alpha }_2$ than Liu's when $\frac{{\alpha }_2}{{\alpha }_1}>0$; secondly, we show ${\alpha }_1+{\alpha }_2=0$ when $\frac{{\alpha }_2}{{\alpha }_1}<0$.

中文翻译：

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某类非线性复微分方程的亚纯解

本文主要关注某类非线性复微分方程$F^n(z)+{磷}_d(z,F)=p_1{e}^{{\alpha }_{1}z}+p_2{e}^{{\alpha }_{2}z},$在哪里$p_1,p_2,{\alpha }_1,{\alpha }_2$是非零常数和${磷}_d(z,F)$是f中最多n -1 次的d次微分多项式。对于这种方程，如果它承认一个亚纯解，使得$ñ(r,F)=\mathrm{小号}(r,F)$, 那么我们首先对李的问题给予肯定的回答, 限制较弱${\alpha }_1$和${\alpha }_2$比刘的时候$\frac{{\alpha }_2}{{\alpha }_1}>0$; 其次，我们展示${\alpha }_1+{\alpha }_2=0$什么时候$\frac{{\alpha }_2}{{\alpha }_1}<0$.