关于$\mathbf{C}^2$中的广义Fermat丢番图泛函和偏微分方程
On generalized Fermat Diophantine functional and partial differential equations in $\mathbf{C}^2$
摘要：
在本文中，我们刻画了广义Fermat丢番图函数方程$h(z_1,z_2)f^m+k(z_1,z_2)g^n=1$在$\mathbf{C}^2$中的亚纯解$f(z_1,z_2),g(z_1,z_2)$，对于整数$m,n\geq2$和非零亚纯函数$h(z_1,z_2),k(z_1,z_2)$在$\mathbf{C}^2$中.研究了相应的偏微分方程的亚纯解。
英文摘要：
In this paper, we characterize meromorphic solutions $f(z_1,z_2),g(z_1,z_2)$ to the generalized Fermat Diophantine functional equations $h(z_1,z_2)f^m+k(z_1,z_2)g^n=1$ in $\mathbf{C}^2$ for integers $m,n\geq2$ and nonzero meromorphic functions $h(z_1,z_2),k(z_1,z_2)$ in $\mathbf{C}^2$. Meromorphic solutions to associated partial differential equations are also studied.
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