Nonlinear fractional magnetic Schrödinger equation: Existence and multiplicity

In this paper we focus our attention on the following nonlinear fractional Schrödinger equation with magnetic fieldε2s(−Δ)A/εsu+V(x)u=f(|u|2)u in RN, where ε>0 is a parameter, s∈(0,1), N≥3, (−Δ)As is the fractional magnetic Laplacian, V:RN→R and A:RN→RN are continuous potentials and f:RN→R is a subcritical nonlinearity. By applying variational methods and Ljusternick-Schnirelmann theory, we prove existence and multiplicity of solutions for ε small.