  The Ginzburg-Landau (GL) functional and the resultant phase diagram in strong
fields where the Pauli paramagnetic depairing is not negligible are examined in
details by assuming the weak coupling BCS model with a $d_{x^2-y^2}$-like
pairing. In contrast to previous works on the same subject for spin-singlet
pairings in which the orbital depairing effect was not treated consistently
with the paramagnetic depairing, the temperature at which the mean field (MF)
transition at $H_{c2}$ changes into a discontinuous one lies much above another
temperature at which the $H_{c2}(T)$ and a second order transition curve
$H_{\rm FFLO}(T)$ between an FFLO-like and the ordinary vortex solids branch,
and $H_{\rm FFLO}(T)$ decreases upon cooling. Based on these MF results,
details of a real phase diagram near $H_{c2}(T)$-line are examined in terms of
Monte Carlo simulation, and it is found that the MF discontinuous transition is
changed due to the fluctuation into a crossover which is nearly discontinuous
in systems with weak enough fluctuation. These results induced by the
paramagnetic depairing are consistent both with recent observations of the MF
discontinuous behavior and $H_{\rm {FFLO}}(T)$ in the heavy fermion
superconductor CeCoIn$_5$ with weak fluctuation and with their absence in
organic materials with strong fluctuation.
