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Entire solutions for some critical equations in the Heisenberg group

Pucci Patrizia, Temperini Letizia

Opuscula Mathematica

2022

Vol. 42, no. 2

279--303

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.

Concentration compactness results for systems in the Heisenberg group

Pucci Patrizia, Temperini Letizia

Opuscula Mathematica

2020

Vol. 40, no. 1

151--163

In this paper we complete the study started in [P. Pucci, L. Temperini, Existence for (p,q) critical systems in the Heisenberg group, Adv. Nonlinear Anal. 9 (2020), 895-922] on some variants of the concentration-compactness principle in bounded PS domains Ω of the Heisenberg group [formula]. The concentration-compactness principle is a basic tool for treating nonlinear problems with lack of compactness. The results proved here can be exploited when dealing with some kind of elliptic systems involving critical nonlinearities and Hardy terms.