On degenerate fractional Schrödinger–Kirchhoff–Poisson equations with upper critical nonlinearity and electromagnetic fields

This paper intends to study the following degenerate fractional Schrödinger–Kirchhoff–Poisson equations with critical nonlinearity and electromagnetic fields in R3: {ε2sM([u]s,A2)(−Δ)Asu+V(x)u+ϕu=k(x)|u|r−2u+(Iμ∗|u|2s♯)|u|2s♯−2u,x∈R3,(−Δ)tϕ=u2,x∈R3, where ε>0 is a positive parameter, 3/4<s<1, 0<t<1, V an electric potential satisfying suitable assumptions, 0<k∗≤k(x)≤k∗, Iμ(x)=|x|3−μ 0<μ<3, 2s♯=3+μ3−2s 2<r<2s♯. With help of concentration compactness principle variational method, together some careful analytical skills, we prove existence multiplicity solutions for above problem as ε→0 cases, that Kirchhoff term M can vanish at zero.