On an electromagnetic Schrodinger equation with critical growth

In this paper we consider the electromagnetic Schrodinger problem (-i del +A)(2)u, +lambda V(x)u = K(x)vertical bar v vertical bar(2*-2)u, in H(A,V+)(1)(R(N)) (see the definition in Section 1). According as whether the indefinite linear is resonant or nonresonant, we structure different direct sums of H(A,V+)(1) (R(N)). Then by applying the linking theorem twice to the corresponding functional we establish the existence results. (C) 2007 Elsevier Ltd. All rights reserved.