  We study an eigenvalue problem for the infinity-Laplacian on bounded domains.
We prove the existence of the principal eigenvalue and a corresponding positive
eigenfunction. The work also contains existence results when the parameter, in
the equation, is less than the first eigenvalue. A comparison principle
applicable to these problems is also proven. Some additional results are shown,
in particular, that on star- shaped domains and on C^2 domains higher
eigenfunctions change sign. When the domain is a ball, we prove that the first
eigenfunction has one sign, radial principal eigenfunction exist and are unique
up to scalar multiplication, and that there are infinitely many eigenvalues.
