  We study numerically a parametrically driven discrete nonlinear Schr\"odinger
equation modelling periodically curved waveguide arrays. We show that discrete
surface solitons persist, but their threshold power is altered by the drive.
There are critical drives at which the threshold values vanish. We also show
that parametric drives can create resonance with a phonon making a new barrier
for discrete solitons. By calculating the corresponding Floquet multipliers, we
find that the stability of symmetric and antisymmetric off-side discrete
surface solitons switches approximately at the critical drives for
thresholdless solitons.
