Quasilinear Equations with Exponential Reactions and Measure Data on Carnot Groups

Abstract

In this paper, we establish existence and pointwise Wolff potential bounds for nonnegative solutions of $-{\Delta }_{\mathbb{G},p}u=H_l(\alpha u^{\beta })+\mu$ on Carnot groups, where $H_l(t)=e^t-{\sum }_{j=0}^{l-1}{t}^j/j!$ and $\mu$ 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.

arXiv comment20 pages