  The measurements on a few pentaquarks states $P_c(4440)$, $P_c(4457)$ and
$P_{cs}(4459)$ excite our new interests about their structures. Since the
masses of $P_c(4440)$ and $P_c(4457)$ are close to the threshold of
$\Sigma_c\bar D^*$, in the earlier works, they were regarded as molecular
states of $\Sigma_c\bar D^*$ with quantum numbers
$I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ and $\frac{1}{2}(\frac{3}{2}^-)$,
respectively. In a similar way $P_{cs}(4459)$ is naturally considered as a
$\Xi_c\bar D^*$ bound state with $I=0$. Within the Bethe-Salpeter (B-S)
framework we systematically study the possible bound states of $\Lambda_c\bar
D^*$, $\Sigma_c\bar D^*$, $\Xi_c\bar D^*$ and $\Xi_c'\bar D^*$. Our results
indicate that $\Sigma_c\bar D^*$ can form a bound state with
$I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$, which corresponds to $P_c(4440)$. However
for the $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$ system the attraction between
$\Sigma_c$ and $\bar D^*$ is too weak to constitute a molecule, so
$P_{c}(4457)$ may not be a bound state of $\Sigma_c\bar D^*$ with
$I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$. As $\Xi_c\bar D^*$ and $\Xi_c'\bar D^*$
systems we take into account of the mixing between $\Xi_c$ and $\Xi'_c$ and the
eigenstets should include two normal bound states $\Xi_c\bar D^*$ and
$\Xi_c'\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ and a loosely bound
state $\Xi_c\bar D^*$ with $I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$. The conclusion
that two $\Xi_c\bar D^*$ bound states exist, supports the suggestion that the
observed peak of $P_{cs}(4459)$ may hide two states $P_{cs}(4455)$ and
$P_{cs}(4468)$. Based on the computations we predict a bound state $\Xi_c'\bar
D^*$ with $I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$ but not that with
$I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$. Further more accurate experiments will
test our approach and results.
