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AN EIGENVALUE PROBLEM INVOLVING A FUNCTIONAL DIFFERENTIAL EQUATION ARISING IN A CELL GROWTH MODEL

Part of: Functional-differential and differential-difference equations

Published online by Cambridge University Press:  04 January 2011

BRUCE VAN BRUNT  and
M. VLIEG-HULSTMAN
BRUCE VAN BRUNT*
Affiliation:
Institute of Fundamental Sciences, Mathematics, Massey University, Palmerston North, New Zealand (email: b.vanbrunt@massey.ac.nz)
M. VLIEG-HULSTMAN
Affiliation:
Institute of Fundamental Sciences, Mathematics, Massey University, Palmerston North, New Zealand (email: b.vanbrunt@massey.ac.nz)
*
✉For correspondence; e-mail: b.vanbrunt@massey.ac.nz
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Abstract

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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.

Keywords

pantograph equationcell growth model

MSC classification

Secondary: 34K06: Linear functional-differential equations
Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 4 , April 2010 , pp. 383 - 393
Copyright
Copyright © Australian Mathematical Society 2010

References

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