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

Year 2021, Volume: 5 Issue: 2, 232 - 239, 30.06.2021

Gaurav Dwivedi

https://doi.org/10.31197/atnaa.777775

Cited By: 1

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

Supporting Institution

Science and Engineering Research Board, India

Project Number

MTR/2018/000233

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