In this paper we study the existence, the stability properties, and the bif
urcation structure of static localized solutions in one dimension, near the
robust existence of stable fronts between homogeneous solutions and period
ic patterns. We use the qualitative theory of differential equation to rein
terpret the theory of these stable fronts as developed by Pomeau, and then
use the same framework to develop a theory of stationary localized structur
es.