An eigenvalue problem involving a functional differential equation arising in a cell growth model

Abstract

We interpret a boundary-value problem arising in a cell growth model as a singular Sturm–Liouville problem that involves a functional differential equation of the pantograph type. We show that the probability density function of the cell growth model corresponds to the first eigenvalue and that there is a family of rapidly decaying eigenfunctions. doi:10.1017/S1446181110000866