Classification of the FRW universe with a cosmological constant and a
  perfect fluid of the equation of state $p = w\rho$
  We systematically study the evolution of the Friedmann-Robertson-Walker (FRW)
universe coupled with a cosmological constant $\Lambda$ and a perfect fluid
that has the equation of state $p=w\rho$, where $p$ and $\rho$ denote,
respectively, the pressure and energy density of the fluid, and $w$ is an
arbitrary real constant. Depending on the specific values of $w,\; \Lambda$,
and the curvature $k$ of 3-dimensional space, we separate all of the solutions
into various cases. In each case the main properties of the evolution are given
in detail, including the periods of deceleration and/or acceleration, and the
existence of big bang, big crunch, and big rip singularities. In some cases,
errors in classification and interpretation appearing in standard textbooks
have been corrected.
