(untitled) (Journal of Partial Differential Equations, 2025)
In this paper, we consider the following critical Choquard equation-Δ u = μ f(x)|u|^p-2u + ( _Ω g(y)|u(y)|^6-v |x-y|^v dy ) g(x)|u|^4-vu, x Ω,where µ>0 is a parameter, ν∈(0,3), p∈(4,6) and f ,g are continuous functions. For µ small enough, by using Lusternik-Schnirelmann category theory, we establish a relationship between the number of solutions and the category of the global maximum set of g.