# American Institute of Mathematical Sciences

2005, 2005(Special): 546-555. doi: 10.3934/proc.2005.2005.546

## Properties of kernels and eigenvalues for three point boundary value problems

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

Received  September 2004 Revised  February 2005 Published  September 2005

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.
Citation: K. Q. Lan. Properties of kernels and eigenvalues for three point boundary value problems. Conference Publications, 2005, 2005 (Special) : 546-555. doi: 10.3934/proc.2005.2005.546
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