Asymptotically linear magnetic fractional problems

The aim of this paper is investigating the existence and multiplicity of weak solutions to non–local equations involving the {\em magnetic fractional Laplacian}, when the nonlinearity is subcritical and asymptotically linear at infinity. We prove existence and multiplicity results by using variational tools, extending to the magnetic local and non–local setting some known results for the classical and the fractional Laplace operators.