A Detailed Study of Kirchhoff-type Critical Elliptic Equations and $p$-Sub-Laplacian Operators within the Heisenberg Group ${\mathcal{H}}_n$ Framework

Abstract

This article presents a comprehensive study of \textit{Kirchhoff-type Critical Elliptic Equations} involving $p$-sub-Laplacian Operators on the \textit{Heisenberg Group} ${\mathcal{H}}_n$. It delves into the mathematical framework of Heisenberg Group, and explores their Spectral Properties. A significant focus is on the existence and multiplicity of solutions under various conditions, leveraging concepts like the \textit{Mountain Pass Theorem}. This work not only contributes to the theoretical understanding of such groups but also has implications in fields like Quantum Mechanics and Geometric Group Theory.

29 Pages

References in corpus (2)

• A primer on Carnot groups: homogenous groups, CC spaces, and regularity of their isometries
• A Detailed Study of Kirchhoff-type Critical Elliptic Equations and $p$-Sub-Laplacian Operators within the Heisenberg Group ${\mathcal{H}}_n$ Framework

Cited by in corpus (1)

• A Detailed Study of Kirchhoff-type Critical Elliptic Equations and $p$-Sub-Laplacian Operators within the Heisenberg Group ${\mathcal{H}}_n$ Framework