SOLUTIONS OF PERTURBED SCHRODINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND CRITICAL NONLINEARITY

We consider the existence and multiplicity of standing-wave solutions psi(x, t) = exp (-iEt/(h) over bar )u(x) of nonlinear Schrodinger equations with electromagnetic fields and critical nonlinearity i (h) over bar partial derivative psi/partial derivative t = -(h) over bar (2)/2m (del +iA(x))(2)psi + W(x)psi -K(x)vertical bar psi vertical bar(2)* (-2)psi-h(x,vertical bar psi vertical bar(2))psi, (t, x) is an element of RxR(N), N >= 3. Under suitable assumptions, we prove that it has at least one solution and that, for any m is an element of N, it has at least in pairs of solutions.