  We study analytical properties of the Stuckelberg holographic superconductors
with Weyl corrections. We obtain the minimum critical temperature as a function
of the mass of the scalar field $m^2$. We show that in limit of the
$m^2=-3$,$T^{Min}_c\approx0.158047\sqrt[3]{\rho}$ which is close to the
numerical estimate $T_c^{Numerical}\approx 0.170\sqrt[3]{\rho}$. Further we
show that the mass of the scalar field in bounded from below by the $
m^2>m_c^2$ where $m_c^2=-5.40417$. This lower bound is weaker and different
from the previous lower bound $m^2=-3$ predicted by stability analysis. We show
that in the Breitenlohner-Freedman bound, the critical temperature remains
finite. Explicitly, we prove that here there is exist a linear relation between
$<O_{\Delta}>$ and the chemical potential.
