Multiple solutions for Schrödinger equations with magnetic field

The authors consider the semilinear Schrödinger equation -ΔAu+Vλ(x)u=Q(x)|u|y-1u in ℝN,-ΔAu+Vλ(x)u=Q(x)|u|y-1u in ℝN,where 1 < γ < 2* and γ ≠ 2, Vλ = V+ − λV−. Exploiting the relation between the Nehari manifold and fibrering maps, the existence of nontrivial solutions for the problem is discussed.