  In the strong coupling Bose-Einstein Condensation (BEC) regime the
superconductors have two characteristic temperatures: $T^*$- onset of fermion
pairing and $T_{sc}$- onset of superconductivity, such that $T_{sc}<T^*$. In
the present article, we consider time dependent Ginzburg-Landau theory of
superconductors with slab geometry and show that applied electric field, in the
temperature interval $(T_{sc},T^*)$, Bose condenses the Cooper pairs thereby
increasing the superconductor critical temperature $T^E_{sc}>T_{sc}$. Important
consequence is the fact that arbitrary temperature within the interval
($T_{sc},T^*$) is a critical temperature of superconductor transition if an
appropriate electric field is applied. This means that if we set the
temperature of the system within the above mentioned interval and increase the
applied electric field the system undergoes an electric field induced
transition to superconductor.
  We also show the existence of critical value of the applied electric field at
which $T^*=T^E_{sc}$. This means that although the system is in BEC regime,
  away from the BCS one, we can apply an electric field that moves the system
to a state with $T^E_{sc}=T^*$, characteristic of BCS regime. The results
indicate that applied electric field experiments are a suitable tool to
identify the BEC regime of the superconductors. The experiment can determine
$T^*$ as a temperature below which the electric field Bose condenses the Cooper
pairs, while above it the electrons screen the field and it cannot penetrate.
