  We study the bound states of a Kronig Penney potential for a nonlinear
one-dimensional Schroedinger equation. This potential consists of a large, but
not necessarily infinite, number of equidistant delta-function wells. We show
that the ground state can be highly degenerate. Under certain conditions
furthermore, even the bound state that would normally be the highest can have
almost the same energy as the ground state. This holds for simple periodic
potentials as well.
