Ground‐state solutions of Schrödinger‐type equation with magnetic field

Abstract

In this paper, the nonlinear Schrödinger‐type equation is considered in the presence of magnetic field, where , , denotes the Riesz potential, is a positive potential for some , is a nonnegative potential for some , and is assumed to be asymptotically linear at infinity. Under suitable assumptions regarding , , , and , variational methods are used to establish the existence of ground‐state solutions of the above equation for sufficiently small values of the parameter .