On concentration of least energy solutions for magnetic critical Choquard equations

In the present paper, we consider the following magnetic nonlinear Choquard equation{(−i∇+A(x))2u+μg(x)u=λu+(|x|−α⁎|u|2⁎α)|u|2α⁎−2uinRn,u∈H1(Rn,C) where n≥4, 2α⁎=2n−αn−2, α∈(0,n), μ>0, λ>0 is a parameter, A(x):Rn→Rn is a magnetic vector potential and g(x) is a real valued potential function on Rn. Using variational methods, we establish the existence of least energy solution under some suitable conditions. Moreover, the concentration behavior of solutions is also studied as μ→+∞.