Ground state solutions for the Kirchhoff–Choquard type equation with lower critical exponent

In this paper, we study the Kirchhoff–Choquard type equation −(a+b∫R3|∇u|2dx)Δu+V(x)u=(Iα∗G(u))g(u),u∈H1(R3), where a, b>0, g(u)=|u|p_−2u+1p_h(u), G(u)=p_∫0ug(s)ds=|u|p_+H(u), p_=3+α3 is the lower critical Hardy–Littlewood–Sobolev exponent and Iα is the Riesz potential. Under certain assumptions on V and h, we prove that the above problem admits a ground state solution by using variational methods.