  The main goal of this paper is twofold. First, it characterizes the existence
of positive periodic solutions for a general class of weighted
periodic-parabolic logistic problems of degenerate type (see (1.1)). This
result provides us with is a substantial generalization of Theorem 1.1 of
Daners and L\'opez-G\'omez [12] even for the elliptic counterpart of (1.1), and
of some previous findings of the authors in [1] and [2]. Then, it sharpens some
results of [19] by enlarging the class of critical degenerate weight functions
for which (1.1) admits a positive periodic solution in an unbounded interval of
values of the parameter $\lambda$. The latest findings, not having any previous
elliptic counterpart, are utterly new and of great interest in Population
Dynamics.
