  In the framework of Horava-Lifshitz theory, we study the eigenvalues
associated with the Wheeler-DeWitt equation representing the vacuum expectation
values associated with the cosmological constant. The explicit calculation is
performed with the help of a variational procedure with trial wave functionals
of the Gaussian type. We analyze both the case with the detailed balanced
condition and the case without it. In the case without the detailed balance, we
find the existence of an eigenvalue depending on the set of coupling constants
(g2,g3) and (g4,g5,g6), respectively, and on the physical scale.
