A note on Kirchhoff-type equations with Hartree-type nonlinearities

We consider the following Kirchhoff-type equation in R3R3−(a+b∫R3|∇u|2dx)Δu+(1+μg(x))u=(1|x|α∗|u|p)|u|p−2u, where a>0a>0, b≥0b≥0 are constants, α∈(0,3)α∈(0,3), p∈(2,6−α)p∈(2,6−α), μ>0μ>0 is a parameter and g(x)g(x) is a nonnegative continuous potential satisfying some conditions. By using the Nehari manifold and the concentration compactness principle, we establish the existence of ground state solutions for the equation if the parameter μμ is large enough. Moreover, some concentration behaviors of these solutions as μ→+∞μ→+∞ are discussed.