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

TL;DR

This paper investigates the existence and uniqueness of positive solutions to a quasilinear elliptic equation involving the p-Laplacian in the Heisenberg group, utilizing Diaz-Saa inequality and a generalized Picone's identity.

Contribution

It introduces a generalized Picone's identity in the Heisenberg group to establish the uniqueness of positive solutions for the p-Laplacian equation.

Findings

Proved the uniqueness of positive solutions using Diaz-Saa inequality.

Established a generalized Picone's identity in the Heisenberg group.

Provided conditions for existence and uniqueness of solutions.

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-Saa Inequality in Heisenberg Group which we obtain via a generalized version of Picone's Identity.