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
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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- Patrizia Pucci
https://orcid.org/0000-0001-7242-8485
- Università degli Studi di Perugia, Dipartimento di Matematica e Informatica, Via Vanvitelli 1, 06123 Perugia, Italy
- Communicated by Vicentiu D. Radulescu.
- Received: 2018-08-10.
- Accepted: 2018-10-29.
- Published online: 2018-12-07.