A Detailed Study of Kirchhoff-type Critical Elliptic Equations and p-Sub-Laplacian Operators within the Heisenberg Group Hn Framework

Subham De

Abstract: This article presents a comprehensive study of Kirchho?-type Critical Elliptic Equations involving p-sub-Laplacian Operators on the Heisenberg Group Hn. It delves into the mathematical framework of Heisenberg Group, and explores their Spectral Properties. A signifcant focus is on the existence and multiplicity of solutions under various conditions, leveraging concepts like the Mountain Pass Theorem. This work not only contributes to the theoretical understanding of such groups but also has implications in felds like Quantum Mechanics and Geometric Group Theory.

Keywords: Heisenberg Group, sub-Laplacian, Twisted laplacian, Essential Self-Adjointness, Spectrum, Essential Spectra, p-sub-Laplacian, Kirchho?-type Critical Elliptic Equations, Palais-Smale Condition

How to Cite?: Subham De, "A Detailed Study of Kirchhoff-type Critical Elliptic Equations and p-Sub-Laplacian Operators within the Heisenberg Group Hn Framework", Volume 12 Issue 12, December 2023, International Journal of Science and Research (IJSR), Pages: 7-35, https://www.ijsr.net/getabstract.php?paperid=SR231130204147, DOI: https://dx.doi.org/10.21275/SR231130204147