Existence of nontrivial solutions for fractional Choquard equations with critical or supercritical growth. Issue 3 (11th February 2022) - Li, Quanqing; Zhang, Jian; Wang, Wenbo; Teng, Kaimin
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.