(p,Q) systems with critical singular exponential nonlinearities in the Heisenberg group

Abstract

Abstract The paper deals with the existence of solutions for ( p , Q ) (p,Q) coupled elliptic systems in the Heisenberg group, with critical exponential growth at infinity and singular behavior at the origin. We derive existence of nonnegative solutions with both components nontrivial and different, that is solving an actual system, which does not reduce into an equation. The main features and novelties of the paper are the presence of a general coupled critical exponential term of the Trudinger-Moser type and the fact that the system is set in ℍ n {{\mathbb{H}}}^{n} .