Intertwining solutions for magnetic relativistic Hartree type equations

We consider the magnetic pseudo-relativistic Schrodinger equation root(-i del -A(x))(2) + m(2)u + V(x) u = (I-alpha * vertical bar u vertical bar(p)) vertical bar u vertical bar(p-2)u, in R-N where N >= 3, m > 0, V : R-N -> R is an external continuous scalar potential, A: R-N -> R-N is a continuous vector potential and I-alpha(x) = c(N,alpha)/vertical bar x vertical bar(N-alpha) (x not equal 0) is a convolution kernel, c(N,alpha) > 0 is a constant, 2 <= p < 2N/(N - 1), (N -1) p - N < alpha < N. We assume that A and V are symmetric with respect to a closed subgroup G of the group O(N) of orthogonal linear transformations of R-N. If for any x is an element of R-N\{0}, the cardinality of the G-orbit of x is infinite, then we prove the existence of infinitely many intertwining solutions assuming that A(x) is either linear in x or uniformly bounded. The results are proved by means of a new local realization of the square root of the magnetic laplacian to a local elliptic operator with Neumann boundary condition on a half-space. Moreover we derive an existence result of a ground state intertwining solution for bounded vector potentials, if G admits a finite orbit.