Entire solution of a partial differential equation

In this paper, using Nevanlinna’s value distribution theory of meromorphic functions in several complex variables, we study for the existence of entire solutions $f$ in ${\mathbb{C}}^2$ of the following partial differential equation $$a_1{\left(\frac{\mathrm{\partial }f(z_1,z_2)}{\mathrm{\partial }{z}_1}\right)}^n+a_2{f}^n(z_1,z_2)=p_1{e}^{r(z_1,z_2)}+p_2{e}^{s(z_1,z_2)},$$ where $n$ is a positive integer such that $n\ge 3$, $a_1,a_2,p_1,p_2$ are non-zero constants and $r(z_1,z_2),s(z_1,z_2)$ are arbitrary polynomials in ${\mathbb{C}}^2$.