Uniqueness of positive solution for a quasilinear elliptic equation in heisenberg group

Abstract

In this article we are interested in addressing the question of existence and uniqueness of positive solution to a quasilinear elliptic equation involving p-laplacian in Heisenberg Group. The idea is to prove the uniqueness by using Diaz-Saá Inequality in Heisenberg Group which we obtain via a generalized version of Picone's Identity.