The solution of eigenvalue problems for partial differential operators by
using boundary integral equation methods usually involves some Newton potentials
which may be resolved by using a multiple reciprocity approach. Here we propose
an alternative approach which is in some sense equivalent to the above. Instead of a
linear eigenvalue problem for the partial differential operator we consider a nonlinear
eigenvalue problem for an associated boundary integral operator. This nonlinear
eigenvalue problem can be solved by using some appropriate iterative scheme, here
we will consider a Newton scheme.We will discuss the convergence and the boundary
element discretization of this algorithm, and give some numerical results.