  We investigate stationary solutions of a non-local aggregation equation with
degenerate power-law diffusion and bounded attractive potential in arbitrary
dimensions. Compact stationary solutions are characterized and compactness
considerations are used to derive the existence of global minimizers of the
corresponding energy depending on the prefactor of the degenerate diffusion for
all exponents of the degenerate diffusion greater than one. We show that a
global minimizer is compactly supported and, in case of quadratic diffusion, we
prove that it is the unique stationary solution up to a translation. The
existence of stationary solutions being only local minimizers is discussed.
