Existence and multiplicity results for quasilinear equations in the Heisenberg group

Abstract

In this paper we complete the study started in [Existence of entire solutions for quasilinear equations in the Heisenberg group, Minimax Theory Appl. 4 (2019)] on entire solutions for a quasilinear equation \((\mathcal{E}_{\lambda})\) in \(\mathbb{H}^{n}\), depending on a real parameter \(\lambda\), which involves a general elliptic operator \(\mathbf{A}\) in divergence form and two main nonlinearities. Here, in the so called sublinear case, we prove existence for all \(\lambda\gt 0\) and, for special elliptic operators \(\mathbf{A}\), existence of infinitely many solutions \((u_k)_k\).

Keywords

• heisenberg group
• entire solutions
• critical exponents