Existence of bound and ground states for an elliptic system with double criticality. (March 2022)

• Record Type: Journal Article
• Authors: Colorado, Eduardo; López-Soriano, Rafael; Ortega, Alejandro
• Is Part Of: Nonlinear analysis. Volume 216(2022)
• Publication Date: 2022-03
• Subjects: primary 35J47 35J50 35J60 35Q55; Systems of elliptic equations -- Variational methods -- Ground states -- Bound states -- Compactness principles -- Critical Sobolev -- Hardy potential -- Doubly critical problems; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112730
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the existence of bound and ground states for a class of nonlinear elliptic systems in R N . These equations involve critical power nonlinearities and Hardy-type singular potentials, coupled by a term containing up to critical powers. More precisely, we find ground states if either the positive coupling parameter ν is large or ν is small under suitable assumptions on the other parameters of the problem. Furthermore, bound states are found as Mountain-Pass-type critical points of the underlying functional constrained on the Nehari manifold. Our variational approach improves some known results and allows us to cover ranges of parameters which have not been considered previously.