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

Let [Formula: see text] be a stratified Lie group of homogeneous dimension [Formula: see text] The purpose of this 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 text] [Formula: see text] [Formula: see text] [Formula: 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.