Opuscula Math. 39, no. 2 (2019), 247-257
https://doi.org/10.7494/OpMath.2019.39.2.247

Opuscula Mathematica

# Existence and multiplicity results for quasilinear equations in the Heisenberg group

Patrizia Pucci

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.

Mathematics Subject Classification: 35J62, 35J70, 35B08, 35J20, 35B09.

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• Communicated by Vicentiu D. Radulescu.
• Accepted: 2018-10-29.
• Published online: 2018-12-07.