Abstract
We study the field equation -Deltau + V(x)u + epsilon (-Delta (p)u + W'(u)) = mu mu on a bounded domain and on Rn, with E 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 E sufficiently small, there exists a finite number of solutions (mu (epsilon), mu(epsilon)) of the eigenvalue problem for any given charge q is an element of Z {0}.