- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 5 Issue: 2
- Generalised Picone's identity and some Qualitative properties of p-sub-Laplacian on Heisenberg group
Generalised Picone's identity and some Qualitative properties of p-sub-Laplacian on Heisenberg group
Authors : Gaurav DWİVEDİ
Pages : 232-239
Doi:10.31197/atnaa.777775
View : 4 | Download : 2
Publication Date : 2021-06-30
Article Type : Research
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.Keywords : Picone' Identity, Heisenberg Group, Hardy type inequality, Picone's Inequality