Existence and asymptotic behavior of ground state solutions for a class of magnetic kirchhoff choquard type equation with a steep potential well

In this paper, we consider the following nonlinear magnetic Kirch-hoff Choquard type equation [a+b integral RN(|del Au|2+lambda V(x)|u|2)dx](-triangle Au+lambda V(x)u) =(I alpha & lowast;F(|u|))f(|u|)|u|u,inR(N), where u:R-N -> C,A:R-N -> R(N )is a vector potential,N >= 3,a >0,b >0,alpha is an element of(N-2,N],V:RN -> Ris a scalar potential function andI alpha is a Rieszpotential of order alpha is an element of(N-2,N]. Under certain assumptions onA(x),V(x)andf(t), we prove that the equation has at least one ground state solution byvariational methods and investigate the asymptotic behavior of solutions.