  Possible ordered states in the 2D extended Hubbard model with on-site (U>0)
and nearest-neighbor (V) interaction are examined near half filling, with
emphasis on the effect of finite V. First, the phase diagram at absolute zero
is determined in the mean field approximation. For $V<0$, a state where
d_{x^{2}-y^{2}}-wave superconductivity (dSC), commensurate spin-density-wave
(SDW) and $\pi$-triplet pair coexist is seen to be stabilized. Here, the
importance of $\pi$-triplet pair on the coexistence of dSC and SDW is
indicated. This coexistent state is hampered by the phase separation (PS),
which is generally expected to occur in the presence of finite-range attractive
interaction, but survives. For V>0, a state where commensurate
charge-density-wave (CDW), SDW and ferromagnetism (FM) coexist is seen to be
stabilized. Here, the importance of FM on the coexistence of CDW and SDW is
indicated. Next, in order to examine the effects of fluctuation on each mean
field ordered state, the renormalization group method for the special case that
the Fermi level lies just on the saddle points, ($\pi$,0) and (0,$\pi$), is
applied. The crucial difference from the mean field result is that
superconductivity can arise even for U>0 and $V\geq0$, where the
superconducting gap symmetry is d_{x^{2}-y^{2}}-wave for U>4V and s-wave for
U<4V. Finally, the possibilities that the mean field coexistent states survive
in the presence of fluctuation are discussed.
