In this article,~we study the meromorphic solutions of the following non-linear differential equation $\begin{equation*} f^{n}(z)+P_{d}(z,f)=\sum_{j=1}^{k}p_{j}{\rm e}^{\alpha_{j}z}, \end{equation*}$ where $n$ and $k$ are integers with $n\geq k\geq 3$, $P_{d}(z,f)$ is a differential polynomial in $f$ of degree $d\leq n-1$, $p_{j}'s$ and $\alpha_{j}'s$ are non-zero constants. We obtain the expressions of meromorphic solutions of the above equations under some restrictions on $\alpha_{j}'s$. Some examples are given to illustrate the possibilities of our results.
Minfeng CHEN
,
Meili LIANG
,
Zongsheng GAO
. MEROMORPHIC SOLUTIONS OF CERTAIN TYPES OF DIFFERENTIAL EQUATIONS WITH $K$ EXPONENTIAL TERMS[J]. Acta mathematica scientia, Series B, 2025
, 45(3)
: 1155
-1168
.
DOI: 10.1007/s10473-025-0321-5
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