Opuscula Math. 42, no. 2 (2022), 279-303
https://doi.org/10.7494/OpMath.2022.42.2.279

 
Opuscula Mathematica

Entire solutions for some critical equations in the Heisenberg group

Patrizia Pucci
Letizia Temperini

Abstract. We complete the study started in the paper [P. Pucci, L.Temperini, On the concentration-compactness principle for Folland-Stein spaces and for fractional horizontal Sobolev spaces, Math. Eng. 5 (2023), Paper no. 007], giving some applications of its abstract results to get existence of solutions of certain critical equations in the entire Heinseberg group. In particular, different conditions for existence are given for critical horizontal \(p\)-Laplacian equations.

Keywords: Heisenberg group, entire solutions, critical exponents.

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

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  • Patrizia Pucci (corresponding author)
  • ORCID iD https://orcid.org/0000-0001-7242-8485
  • Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy
  • Letizia Temperini
  • ORCID iD https://orcid.org/0000-0003-2605-6873
  • Dipartimento di Matematica e Informatica \'Ulisse Dini\', Università degli Studi di Firenze, Viale Morgagni 67/a, 50134 Firenze, Italy
  • Communicated by Vicentiu D. Rădulescu.
  • Received: 2021-10-11.
  • Accepted: 2021-11-03.
  • Published online: 2022-02-25.
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Cite this article as:
Patrizia Pucci, Letizia Temperini, Entire solutions for some critical equations in the Heisenberg group, Opuscula Math. 42, no. 2 (2022), 279-303, https://doi.org/10.7494/OpMath.2022.42.2.279

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