  We do more discussions of holographic s-wave superconductors in the
background of AdS3 spacetime. We analytically compute the holographic
superconductor model with the motion equation has two different characteristic
root on the framework of Maxwell electrodynamics field. We study superconductor
models on the framework of Born-Infeld electrodynamics field and on the
framework of the St\"uckelberg form in the background of AdS3 spacetime.
