Existence for fractional (p, q) systems with critical and Hardy terms in RN. (October 2021)

• Record Type: Journal Article
• Authors: Pucci, Patrizia; Temperini, Letizia
• Is Part Of: Nonlinear analysis. Volume 211(2021)
• Publication Date: 2021-10
• Subjects: 35R11 -- 35J50 -- 35J47 -- 35B33 -- 47G20; Fractional partial differential equations -- Variational methods for elliptic systems -- Second order elliptic systems -- Critical exponents -- Integro-differential operators; 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.2021.112477
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper deals with the existence of entire nontrivial solutions for fractional ( p, q ) systems with critical Hardy terms in R N . Existence of solutions for system ( S ) is derived via the mountain pass lemma, whose application is pretty involved and requires some variants of the concentration–compactness principle of Lions and of the concentration–compactness principle at infinity of Chabrowski for vectorial fractional spaces, here proved. Indeed, the "triple loss of compactness" in ( S ), caused by the simultaneous presence of Hardy and critical terms in the whole R N, forces to study the exact behaviour of the P S sequences, in the spirit of Lions. We also present a simplified version ( S ˜ ) of the main system ( S ), which is anyway interesting, since the existence proof for ( S ˜ ) is simpler and more direct. Finally, both existence theorems improve or complement previous results for fractional ( p, q ) scalar and vectorial problems.