Existence for (p,q) critical systems in the Heisenberg group

This paper deals with the existence of entire nontrivial solutions for critical quasilinear systems (S) in the Heisenberg group Hn , driven by general (p,q) elliptic operators of Marcellini types. The study of (S) requires relevant topics of nonlinear functional analysis because of the lack of compactness. The key step in the existence proof is the concentration–compactness principle of Lions, here proved for the first time in the vectorial Heisenberg context. Finally, the constructed solution has both components nontrivial and the results extend to the Heisenberg group previous theorems on quasilinear (p,q) systems.