- Advances in the Theory of Nonlinear Analysis and its Application
- Volume: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 : 50 | Download : 8
Publication Date : 2021-06-30
Article Type : Research Paper
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.insert ignore into journalissuearticles values(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
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