  The key element in time-dependent density functional theory is the one-to-one
correspondence between the one-particle density and the external potential. In
most approaches this mapping is transformed into a certain type of
Sturm-Liouville problem. Here we give conditions for existence and uniqueness
of solutions and construct the weighted Sobolev space they lie in. As a result
the class of v-representable densities is considerably widened with respect to
previous work.
