  The existence of stationary radial solutions to a partial differential
equation arising in the theory of epitaxial growth is studied. Our results
depend on the size of a parameter that plays the role of the velocity at which
mass is introduced into the system. For small values of this parameter we prove
existence of solutions to this boundary value problem. For large values of the
same parameter we prove nonexistence of solutions. We also provide rigorous
bounds for the values of this parameter which separate existence from
nonexistence. The proofs come as a combination of several differential
inequalities and the method of upper and lower functions.
