Meromorphic Solutions of Certain Types of Non-linear Differential Equations

Abstract

Let $p_1, p_2$ and $\alpha _1, \alpha _2$ be non-zero constants, and $P_d(z, f)$ be a differential polynomial in f of degree d. Li obtained the forms of meromorphic solutions with few poles of the non-linear differential equations $f^n+P_d(z, f)=p_1e^{\alpha _1 z}+p_2e^{\alpha _2 z}$ provided $\alpha _1\ne \alpha _2$ and $d\le n-2$. In this paper, given $d=n-1$, we find the forms of meromorphic solutions with few poles of the above equations under some restrictions on $\alpha _1, \alpha _2$. Some examples are given to illustrate our results.