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.
  • Received: 2018-08-10.
  • Accepted: 2018-10-29.
  • Published online: 2018-12-07.
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Cite this article as:
Patrizia Pucci, Existence and multiplicity results for quasilinear equations in the Heisenberg group, Opuscula Math. 39, no. 2 (2019), 247-257, https://doi.org/10.7494/OpMath.2019.39.2.247

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