Existence for ( p , q ) critical systems in the Heisenberg group

Advances in Nonlinear Analysis

article

Patrizia Pucci¹  Letizia Temperini¹ 

[1] Dipartimento di Matematica e Informatica, Università degli Studi di Perugia

关键词: Heisenberg group;    entire solutions;    quasilinear systems;    subelliptic critical systems;    variational methods;    critical exponents;   

DOI  :  10.1515/anona-2020-0032

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

This paper deals with the existence of entire nontrivial solutions for critical quasilinear systems (?) in the Heisenberg group ℍ n , driven by general ( p , q ) elliptic operators of Marcellini types. The study of (?) requires relevant topics of nonlinear functional analysis because of the lack of compactness. The key step in the existence proof is the concentration–compactness principle of Lions, here proved for the first time in the vectorial Heisenberg context. Finally, the constructed solution has both components nontrivial and the results extend to the Heisenberg group previous theorems on quasilinear ( p , q ) systems.

【 授权许可】

CC BY