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Existence for singular critical exponential (𝑝, 𝑄) equations in the Heisenberg group

  • Patrizia Pucci ORCID logo EMAIL logo and Letizia Temperini ORCID logo
Published/Copyright: May 26, 2021

Abstract

The paper deals with the existence of nontrivial solutions for ( p , Q ) equations in the Heisenberg group H n with critical exponential growth at infinity and a singular behavior at the origin. The main features and novelty of the paper are the above generality on the right-hand side of the equation, the ( p , Q ) growth of the elliptic operator and the fact that the equation is studied in the entire Heisenberg group.

MSC 2010: 35B08; 35B33; 35J20; 35J60; 35R03

Award Identifier / Grant number: Prot_U-UFMBAZ-2020-000761

Funding statement: P. Pucci and L. Temperini are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The manuscript was realized within the auspices of the INdAM-GNAMPA Project 2020 titled Equazioni alle derivate parziali: problemi e modelli (Prot_U-UFMBAZ-2020-000761). P. Pucci was also partly supported by the Fondo Ricerca di Base di Ateneo – Esercizio 2017–2019 of the University of Perugia, named PDEs and Nonlinear Analysis.

  1. Communicated by: Juan Manfredi

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Received: 2020-03-28
Revised: 2021-03-31
Accepted: 2021-04-20
Published Online: 2021-05-26
Published in Print: 2022-07-01

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