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We investigate the transition phenomenon of the universe between a phantomand a non-phantom phases. Particular attention is devoted to the case in whichthe cosmological constant depends on time and is proportional to the square ofthe Hubble parameter. Inhomogeneous equations of state are used and theequation of motion is solved. We find that, depending on the choice of theinput parameters, the universe can transit from the non-phantom to the phantomphase leading to the appearance of singularities. In particular, we find thatthe phantom universe ends in the singularity of type III, unlike the casewithout variable cosmological constant in which the phantom phase endsexclusively in the big rip (singularity of type I). The Cardy-Verlinde formulais also introduced for inhomogeneous equation of state and we find that itsequivalence with the total entropy of the universe, coming from the Friedmannequations, occurs only for special choice of the input parameter $m$ at thepresent time.

Transition between phantom and non-phantom phases with time dependent cosmological constant and Cardy-Verlinde formula