An eigenvalue semiclassical problem for the Schrodinger operator with an electrostatic field

We consider the following system of Schrbdinger-Maxwell equations in the unit ball B-1 of R-3 -h(2)/2m Delta v + e phi v = wv, -Delta phi = 4 pi ev(2) with the boundary conditions u = 0, phi = g on partial derivative B-1, where h, m, e, w > 0, v, phi: B-1 -> R, g: partial derivative B-1 -> R. Such system describes the interaction of a particle constrained to move in B1 with its own electrostatic field. We exhibit a family of positive solutions (v(h),phi(h)) corresponding to eigenvalues w(h) such that v(h) concentrates around some points of the boundary partial derivative B-1 which are minima for g when h -> 0.