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

Bruce van Brunt, Marijcke Vleig-Hulstman


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.



pantograph equation; cell growth model


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.