Nonlinear fractional magnetic Schrodinger equation: Existence and multiplicity

In this paper we focus our attention on the following nonlinear fractional Schrodinger equation with magnetic field epsilon(2s(-)Lambda)(s)(A/epsilon)u + V(x)u = f(broken vertical bar u broken vertical bar(2))u in R-N, where epsilon > 0 is a parameter, s is an element of(0, 1), N >= 3, (- Delta)(s)(A) is the fractional magnetic Laplacian, V: R-N (->) R and A : R-N -> R-N are continuous potentials and f : R-N -> R is a subcritical nonlinearity. By applying variational methods and Ljusternick- Schnirelmann theory, we prove existence and multiplicity of solutions for epsilon small. (C) 2017 Elsevier Inc. All rights reserved.