发表机构
School of Mathematical Science and LPMC, Nankai University; Chern Institute of Mathematics and LPMC, Nankai University（南开大学数学科学学院和LPMC; 南开大学陈省身数学研究所和LPMC）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究Carnot群上带指数反应和测度数据的拟线性方程，建立了非负解的存在性和逐点Wolff势界，覆盖次临界与临界情形。
AI 中文摘要
本文在Carnot群上建立了$-\Delta_{\mathbb{G},p}u=H_l(\alpha u^\beta)+\mu$的非负解的存在性和逐点Wolff势界，其中$H_l(t)=e^t-\sum_{j=0}^{l-1}t^j/j!$，$\mu$是非负Radon测度。在反应参数的适当条件下，我们在次临界范围$1<p<Q$内处理任意开集，并施加最大势条件；在临界情形$p=Q$下处理有界域，并施加小总质量条件。
英文摘要
In this paper, we establish existence and pointwise Wolff potential bounds for nonnegative solutions of $-Δ_{\mathbb{G},p}u=H_l(αu^β)+μ$ on Carnot groups, where $H_l(t)=e^t-\sum_{j=0}^{l-1}t^j/j!$ and $μ$ is a nonnegative Radon measure. Under suitable conditions on the reaction parameters, we treat arbitrary open sets in the subcritical range $1<p<Q$ under a maximal potential condition, and bounded domains in the critical case $p=Q$ under a small total mass condition.
Comments20 pages
