CONDENSATION OF THE SCALAR FIELD WITH STUCKELBERG AND WEYL CORRECTIONS IN THE BACKGROUND OF A PLANAR AdS-SCHWARZSCHILD BLACK HOLE

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-c(Min) approximate to 0.158047 3 root rho which is close to the numerical estimate T-c(Numerical) approximate to 0.170 3 root rho. Further we show that the mass of the scalar field is 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 exists a linear relation between < O-Delta > and the chemical potential.