Abstract
We study the field equation
−Δu+V(x)u+εr(−Δpu+W′(u))=μu
on Rn, with ε positive parameter. The function W is singular in a point and so the configurations are characterized by a topological invariant: the topological charge. By a min-max method, for ε sufficiently small, there exists a finite number of solutions (μ(ε),u(ε)) of the eigenvalue problem for any given charge q∈Z∖{0}.