A multiphase eigenvalue problem on a stratified Lie group

TL;DR

This paper investigates a multiphase eigenvalue problem on stratified Lie groups, proving the existence of eigenfunctions and establishing a Pohozaev-like identity specific to the Heisenberg group, advancing spectral theory in this context.

Contribution

It introduces the existence proof for eigenfunctions of a multiphase spectral problem and derives a Pohozaev-like identity on stratified Lie groups, particularly the Heisenberg group.

Findings

Existence of eigenfunctions for the (2,q)-eigenvalue problem.

Derivation of a Pohozaev-like identity on the Heisenberg group.

Extension of spectral problem analysis to stratified Lie groups.

Abstract

We consider a multiphase spectral problem on a stratified Lie group. We prove the existence of an eigenfunction of $(2,q)$-eigenvalue problem on a bounded domain. Furthermore, we also establish a Pohozaev-like identity corresponding to the problem on the Heisenberg group.