  We examine the star formation history and stellar feedback effects of dwarf
galaxies under the influence of extragalactic ultraviolet radiation. We
consider the dynamical evolution of gas in dwarf galaxies using a
one-dimensional, spherically symmetric, Lagrangian numerical scheme to compute
the effects of radiative transfer and photoionization. We include a
physically-motivated star formation recipe and consider the effects of
feedback. Our results indicate that star formation in the severe environment of
dwarf galaxies is a difficult and inefficient process. For intermediate mass
systems, such as the dSphs around the Galaxy, star formation can proceed with
in early cosmic epochs despite the intense background UV flux. Triggering
processes such as merger events, collisions, and tidal disturbance can lead to
density enhancements, reducing the recombination timescale, allowing gas to
cool and star formation to proceed. However, the star formation and gas
retention efficiency may vary widely in galaxies with similar dark matter
potentials, because they depend on many factors, such as the baryonic fraction,
external perturbation, IMF, and background UV intensity. We suggest that the
presence of very old stars in these dwarf galaxies indicates that their initial
baryonic to dark matter content was comparable to the cosmic value. This
constraint suggests that the initial density fluctuation of baryonic matter may
be correlated with that of the dark matter. For the more massive dwarf
elliptical galaxies, the star formation efficiency and gas retention rate is
much higher. Their mass to light ratio is regulated by star formation feedback,
and is expected to be nearly independent of their absolute luminosity. The
results of our theoretical models reproduce the observed $M/L-M_v$ correlation.
