On an electromagnetic Schrödinger equation with critical growth

In this paper we consider the electromagnetic Schrödinger problem (−i∇+A)2u+λV(x)u=K(x)|u|2∗−2u(−i∇+A)2u+λV(x)u=K(x)|u|2∗−2u, in HA,V+1(RN) (see the definition in Section 1). According as whether the indefinite linear is resonant or nonresonant, we structure different direct sums of HA,V+1(RN). Then by applying the linking theorem twice to the corresponding functional we establish the existence results.