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

TL;DR

This paper establishes existence results for certain nonlinear partial differential equations involving the N-Laplacian and N/2-Hessian operators with exponential reaction terms and measure data, expanding the understanding of such equations.

Contribution

It provides new existence theorems for equations with exponential nonlinearities and measure data involving N-Laplacian and N/2-Hessian operators.

Findings

Existence results for N-Laplacian equations with exponential reactions.

Existence results for N/2-Hessian equations with exponential reactions.

Handling measure data in nonlinear PDEs.

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.