Intertwining semiclassical bound states to a nonlinear magnetic Schrodinger equation

We consider the magnetic NLS equation (-epsilon i del + A(x))(2)u + V(x)u = vertical bar u vertical bar(p-2)u, x is an element of R-N, (0.1) where N >= 3, 2 < p < 2* := 2N/(N - 2), A : R-N -> R-N is a magnetic potential and V : R-N -> R is a bounded electric potential. We consider a group G of orthogonal transformations of R-N, and we assume that A(gx) = gA(x) and V (gx) = V (x) for any g is an element of G, x is an element of R-N. Given a group homomorphism tau : G -> S-1 into the unit complex numbers, we show the existence of semiclassical solutions u(epsilon) : R-N -> C to problem (0.1), which satisfy u(epsilon)(gx) = tau(g)u epsilon(x) for all g is an element of G, x is an element of R-N. Moreover, we show that there is a combined effect of the symmetries and the electric potential V on the number of solutions of this type.