Properties of kernels and eigenvalues for three point boundary value problems

K. Q. Lan

doi:10.3934/proc.2005.2005.546

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2005, Volume 2005: 546-555. Doi: 10.3934/proc.2005.2005.546 open access

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Properties of kernels and eigenvalues for three point boundary value problems

K. Q. Lan^1,

1.
Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3

Received: August 31, 2004

Revised: January 31, 2005

Published: August 2005

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Abstract

We investigate the properties of a kernel arising from a three point boundary value problem. We seek a lower bound for the kernel and evaluate the optimal values for the integrals related to the kernel. The smallest positive characteristic value for a linear second ordinary differential equation with a three point boundary condition is estimated by using our lower bound. These optimal values and the estimates for characteristic values are useful in studying the existence of nonzero positive solutions for the boundary value problem.

Keywords:

second order differential equation,
three point boundary condition,
characteristic values,
multiple positive solutions,
Hammerstein integral equation TEX files.

Mathematics Subject Classification: Primary: 34B18; Secondary: 34B15, 34B16, 47H10,47H30.

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