  Formulating the equations of motion for cosmological bodies (such as
galaxies) in an integral, rather than differential, form has several
advantages. Using an integral the mathematical instability at early times is
avoided and the boundary conditions of the integral correspond closely with
available data. Here it is shown that such a least-action calculation for a
number of bodies interacting by gravity has a finite number of solutions,
possibly only one. Characteristics of the different possible solutions are
explored. The results are extended to cover the motion of a continuous fluid. A
method to generalize an action to use velocities, instead of positions, in
boundary conditions, is given, which reduces in particular cases to those given
by Giavalisco et al. (1993) and Schmoldt & Saha (1998). The velocity boundary
condition is shown to have no effect on the number of solutions.
