Liouville theorem and classification of positive solutions for a fractional Choquard type equation. (August 2019)

• Record Type: Journal Article
• Authors: Le, Phuong
• Is Part Of: Nonlinear analysis. Volume 185(2019)
• Page Start: 123
• Page End: 141
• Publication Date: 2019-08
• Subjects: Fractional Choquard equations -- Liouville theorems -- Classification of positive solutions; 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.2019.03.006
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let n ≥ 2, 0 < α < 2 and 0 < β < n . We prove that the equation ( − Δ ) α 2 u = 1 | x | n − β ∗ u p u p − 1 in R n has no positive solution if 1 ≤ p < n + β n − α . We also classify all positive solutions to the equation in the critical case p = n + β n − α .