What question did this study set out to answer?

To establish the existence and multiplicity of weak solutions for nonlocal subelliptic PDEs on stratified Lie groups.

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January 18, 2026Open Access

Nonlocal subelliptic systems involving concave-convex nonlinearities on stratified Lie groups

Key Points

To establish the existence and multiplicity of weak solutions for nonlocal subelliptic PDEs on stratified Lie groups.
Investigated systems of nonlocal nonlinear subelliptic PDEs
Utilized fractional sub-Laplacian
Focused on smooth bounded domains within Lie groups
Applied mathematical techniques to study weak solutions
Proved existence of weak solutions for the proposed system
Demonstrated multiplicity of solutions under certain parameters
Results extend previous research especially for the Heisenberg group

Abstract

Let Formula: see text be a stratified Lie group of homogeneous dimension Formula: see text. The purpose of the present paper is to prove the existence and multiplicity of weak solutions to the following system of nonlocal nonlinear subelliptic PDEs involving fractional Formula: see text-sub-Laplacian Formula: see textFormula: see text where Formula: see text is a smooth bounded domain, Formula: see text are real parameters, Formula: see text, Formula: see text, Formula: see text and Formula: see text is such that Formula: see text. To the best of our knowledge, this is the first work establishing existence and multiplicity results for subelliptic nonlocal systems on stratified Lie groups, which are new even in the case Formula: see text and for the Heisenberg group.

Nonlocal subelliptic systems involving concave-convex nonlinearities on stratified Lie groups

Key Points

Abstract

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