  In this work we introduce and analyze a linear size-structured population
model with infinite states-at-birth. We model the dynamics of a population in
which individuals have two distinct life-stages: an "active" phase when
individuals grow, reproduce and die and a second "resting" phase when
individuals only grow. Transition between these two phases depends on
individuals' size. First we show that the problem is governed by a positive
quasicontractive semigroup on the biologically relevant state space. Then we
investigate, in the framework of the spectral theory of linear operators, the
asymptotic behavior of solutions of the model. We prove that the associated
semigroup has, under biologically plausible assumptions, the property of
asynchronous exponential growth.
