We investigate the transition phenomenon of the universe between a phantom
and a non-phantom phases. Particular attention is devoted to the case in which
the cosmological constant depends on time and is proportional to the square of
the Hubble parameter. Inhomogeneous equations of state are used and the
equation of motion is solved. We find that, depending on the choice of the
input parameters, the universe can transit from the non-phantom to the phantom
phase leading to the appearance of singularities. In particular, we find that
the phantom universe ends in the singularity of type III, unlike the case
without variable cosmological constant in which the phantom phase ends
exclusively in the big rip (singularity of type I). The Cardy-Verlinde formula
is also introduced for inhomogeneous equation of state and we find that its
equivalence with the total entropy of the universe, coming from the Friedmann
equations, occurs only for special choice of the input parameter m at the
present time.Comment: 12 pages, 2 figure
