Meromorphic solutions of some non-linear difference equations with three exponential terms
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In this paper, we study the existence of finite order meromorphic solutions of the following non-linear difference equation \begin{equation*} f^{n}(z)+P_{d}(z,f)=p_{1}e^{\alpha_{1}z}+p_{2}e^{\alpha_{2}z}+p_{3}e^{\alpha_{3}z}, \end{equation*} where $n\geq 2$ is an integer, $P_{d}(z,f)$ is a difference polynomial in $f$ of degree $d\leq n-2$ with small functions of $f$ as its coefficients, $p_{j}~(j=1,2,3)$ are small meromorphic functions of $f$ and $\alpha_{j}~(j=1,2,3)$ are three distinct non-zero constants. We give the expressions of finite order meromorphic solutions of the above equation under some restrictions on $\alpha_{j}~(j=1,2,3)$. Some examples are given to illustrate the accuracy of the conditions.
Abstract
In this paper, we study the existence of finite order meromorphic solutions of the following non-linear difference equation \begin{equation*} f^{n}(z)+P_{d}(z,f)=p_{1}e^{\alpha_{1}z}+p_{2}e^{\alpha_{2}z}+p_{3}e^{\alpha_{3}z}, \end{equation*} where $n\geq 2$ is an integer, $P_{d}(z,f)$ is a difference polynomial in $f$ of degree $d\leq n-2$ with small functions of $f$ as its coefficients, $p_{j}~(j=1,2,3)$ are small meromorphic functions of $f$ and $\alpha_{j}~(j=1,2,3)$ are three distinct non-zero constants. We give the expressions of finite order meromorphic solutions of the above equation under some restrictions on $\alpha_{j}~(j=1,2,3)$. Some examples are given to illustrate the accuracy of the conditions.
참고문헌 (17)
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