Multiplicity results for magnetic fractional problems

The paper deals with the existence of multiple solutions for a boundary value problem driven by the magnetic fractional Laplacian (−Δ)As, that is(−Δ)Asu=λf(|u|)u in Ω,u=0 in Rn∖Ω, where λ is a real parameter, f is a continuous function and Ω is an open bounded subset of Rn with Lipschitz boundary. We prove that the problem admits at least two nontrivial weak solutions under two different sets of conditions on the nonlinear term f which are dual in a suitable sense.