Ground State Solution of Kirchhoff Problems with Hartree Type Nonlinearity

For the Kirchhoff type equation -(a+b integral(R3)vertical bar del u vertical bar vertical bar(2) dx)Delta u+V(x)u=(I alpha*vertical bar u vertical bar(p))vertical bar u vertical bar(p-2)u in R-3, where a, b>0, 0<alpha<3, 2<p<3+alpha and I-alpha is the Riesz potential, we establish the existence of a positive ground state solution by using Nehari manifold technique and concentration compactness argument. The main novelty in our context is that the potential V exhibits a mixed behavior, i.e., V is periodic in some directions while tends to a positive constant in the remaining ones.