Existence of nontrivial solutions for fractional Choquard equations with critical or supercritical growth. Issue 3 (11th February 2022)

• Record Type: Journal Article
• Authors: Li, Quanqing; Zhang, Jian; Wang, Wenbo; Teng, Kaimin
• Is Part Of: Applicable analysis. Volume 101:Issue 3(2022)
• Page Start: 849
• Page End: 857
• Publication Date: 2022-02-11
• Subjects: Fractional Choquard equation -- critical or supercritical growth -- variational method; 35J20 -- 35J70 -- 35P05 -- 35P30 -- 34B15 -- 58E05 -- 47H04; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1761015
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we study the following fractional Choquard equation with critical or supercritical growth 1 ( − Δ ) s u + V ( x ) u = [ | x | − μ ∗ F ( u ) ] f ( u ) + λ [ | x | − μ ∗ | u | p ] p | u | p − 2 u, x ∈ R N, where 0< s <1, ( − Δ ) s denotes the fractional Laplacian of order s, N >2 s, 0 < μ < 2 s and p ≥ 2 μ, s ∗ := ( 2 N − μ ) / ( N − 2 s ) . Under some suitable conditions, we prove that the equation has a nontrivial solution for small λ > 0 by the variational method.