Generalised Picone's identity and some Qualitative properties of p-sub-Laplacian on Heisenberg group

Abstract

In this article, we derive a generalised nonlinear Picone's identity for $p$ sub-Laplacian on the Heisenberg group. Our main result generalises the Picone's identity established by Niu et al.(Proceedings of the American Mathematical Society , Dec., 2001, Vol. 129, No. 12, pp. 3623-3630). As an application of Picone's identity, we prove a Hardy type inequality and Picone's inequality. We also establish some qualitative results involving the system of nonlinear equations involving $p$-sub-Laplacian.