Existence and Multiplicity of Solutions for Nonlocal Schrodinger-Kirchhoff Equations With the External Magnetic Field

We are concerned with the existence of a nontrivial weak solution to Schrdinger-Kirchhoff type equations involving the fractional magnetic field without Ambrosetti and Rabinowitz condition using mountain pass theorem under suitable assumptions of the external force.Also, we present the existence of infinitely many large-or small-energy solutions to this problem.The strategy of the proof for these results is to approach the problem by applying the variational methods, namely, the fountain and the dual fountain theorem with Cerami condition.