Sign-changing solutions to the critical Choquard equation

Abstract

We consider the following Choquard problem −Δu=λu+f(x)(|x|−μ∗|u|2μ∗)|u|2μ∗−2uinΩ,u=0on∂Ω, where 0<λ<λ1(Ω),|Ω|<∞. 2μ∗ is the upper critical exponent in the sense of Hardy–Littlewood–Sobolev inequality. We prove the existence of sign-changing solution by combining Nehari manifold method with the Ljusternik–Schnirelman theory. The main results extend and complement the earlier works (Guo et al., 2019; Moroz and Schaftingen, 2015).