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 $(u_{k})_{k}$.