Eigenfunctions arising from a first-order functional differential equation in a cell growth model

Bruce van Brunt, Marijcke Vlieg-Hulstman (deceased)

Abstract


A boundary-value problem for cell growth leads to an eigenvalue problem. In this paper some properties of the eigenfunctions are studied. The first eigenfunction is a probability density function and is of importance in the cell growth model. We sharpen an earlier uniqueness result and show that the distribution is unimodal. We then show that the higher eigenfunctions have nested zeros. We show that the eigenfunctions are not mutually orthogonal, but that there are certain orthogonality relations that effectively partition the set of eigenfunctions into two sets.

doi:10.1017/S1446181111000575

Keywords


pantograph equation; cell growth model; nonlocal eigenvalue problem



DOI: http://dx.doi.org/10.21914/anziamj.v52i0.3339



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