Ground-state solutions of Schrodinger-type equation with magnetic field

In this paper, the nonlinear Schrodinger-type equation -(del+ iA)(2) u + u + lambda [I-alpha * ( K vertical bar u vertical bar(2))] Ku = af(vertical bar u vertical bar)/vertical bar u vertical bar u in R-3 is considered in the presence of magnetic field, where A epsilon C-1(R-3, R-3), alpha epsilon (0, 3), I-alpha denotes the Riesz potential, K epsilon L-p(R-3) is a positive potential for some p. (6/(1+alpha), infinity], a epsilon L-q(R-3)\{0} is a nonnegative potential for some q epsilon (3/2, infinity], and f epsilon C(R, [0, infinity)) is assumed to be asymptotically linear at infinity. Under suitable assumptions regarding A, K, a, and f, variational methods are used to establish the existence of ground-state solutions of the above equation for sufficiently small values of the parameter lambda.