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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.

Two classes of infinitely many solutions for fractional Schrödinger-Maxwell system with concave-convex power nonlinearities

Khiddi Mustapha

Journal of Mathematics and Applications

2022

Vol. 45

87--105

Employing critical theory and concentration estimates, we establish the existence of two classes of infinitely many weak solutions fractional Schrödinger-Poisson system involving critical Sobolev growth. The first classe of solutions with negative energy is found by using of notion genus while the second one contains infinitely many weak solutions with positive energy via Fountain theorem.

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.

Existence and multiplicity results for quasilinear equations in the Heisenberg group

Pucci Patrizia

Opuscula Mathematica

2019

Vol. 39, no. 2

247--257

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 [formula] in Hn, depending on a real parameter λ, which involves a general elliptic operator A in divergence form and two main nonlinearities. Here, in the so called sublinear case, we prove existence for all λ > 0 and, for special elliptic operators A, existence of infinitely many solutions [formula].