Nonlocal Schrödinger-Kirchhoff equations with external magnetic field

The paper deals with the existence and multiplicity of solutions of the fractional Schrödinger-Kirchhoff equation involving an external magnetic potential and the fractional magnetic operator depending on a matrix A. In the super- and sub-linear cases, the existence of least energy solutions for the above problem is obtained by the mountain pass theorem, combined with the Nehari method, and by the direct methods respectively. In the super- and sub-linear cases, the existence of infinitely many solutions is also investigated by the symmetric mountain pass theorem.