  In loop quantum cosmology, a difference equation for the wave function
describes the evolution of a universe model. This is different from the
differential equations that arise in Wheeler-DeWitt quantizations, and some
aspects of general properties of solutions can appear differently. Properties
of particular interest are boundedness and the presence of small-scale
oscillations. Continued fraction techniques are used to show in different
matter models the presence of special initial conditions leading to bounded
solutions, and an explicit expression for these initial values is derived.
