  We analyze the emergence of classical inflationary universes in a
kinetic-dominated stage using a suitable class of solutions of the Wheeler-De
Witt equation with a constant potential. These solutions are eigenfunctions of
the inflaton momentum operator that are strongly peaked on classical solutions
exhibiting either or both a kinetic dominated period and an inflation period.
Our analysis is based on semiclassical WKB solutions of the Wheeler-De Witt
equation interpreted in the sense of Borel (to perform a correct connection
between classically allowed regions) and on the relationship of these solutions
to the solutions of the classical model. For large values of the scale factor
the WKB Vilenkin tunneling wavefunction and the Hartle-Hawking no-boundary
wavefunctions are recovered as particular instances of our class of
wavefunctions.
