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

Shiguang Ma; Zijian Wang

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

Analysis of PDEs 2024-07-12 v1

Authors: Shiguang Ma , Zijian Wang

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.

Keywords

N-Laplacian N/2-Hessian equation Exponential reaction term Measure data Dirichlet boundary condition Existence result

Cite

@article{arxiv.2407.08266,
  title  = {$N$ -Laplacian and $N/2$-Hessian type equations with exponential reaction term and measure data},
  author = {Shiguang Ma and Zijian Wang},
  journal= {arXiv preprint arXiv:2407.08266},
  year   = {2024}
}

Comments

15pages

Related papers

View all related →