$N$ -Laplacian and $N/2$-Hessian type equations with exponential reaction term and measure data

Abstract

In this article, we will prove existence results for the equations of the type $-{\Delta }_{N}u=H_l(u)+\mu$ and $F_{\frac{N}{2}}[-u]=H_l(u)+\mu$ in a bounded domain $\Omega$, with Dirichlet boundary condition, where the source term $H_l(r)$ takes the form $e^r-{\sum }_{j=0}^{l-1}\frac{r^j}{j!}$ and $\mu$ is a nonnegative Radon measure.

15pages