Entire solutions of $(u_{z_{1}})^{m}+(u_{z_{2}})^{n}=e^{g}$

Abstract

The paper is concerned with description of entire solutions of the partial differential equations $u_{z_{1}}^{m}+u_{z_{2}}^{n}=e^{g}$, where $m \geq 2$, $n \geq 2$ are integers and $g$ is a polynomial or an entire function in ${\bf C}^{2}$. Descriptions are given and complemented by various examples.