The Nehari manifold for a fractional critical Choquard equation involving sign-changing weight functions

Abstract

In this paper, we prove the existence and multiplicity of nontrivial solutions for the following fractional Choquard equation with critical exponent (−Δ)su=λf(x)|u|q−2u+g(x)∫Ω|u|2μ,s∗|x−y|μdy|u|2μ,s∗−2uinΩu=0,inRn∖Ωwhere Ω is a bounded domain in Rn with smooth boundary, s∈(0,1),0<μ<n,n>2s,1<q<2 and 2μ,s∗=(2n−μ)∕(n−2s) is the critical exponent in the sense of Hardy–Littlewood–Sobolev inequality. λ>0 is a parameter and f,g:Ω̄→R are continuous functions but may change sign on Ω.