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Summary: Journal of Computational and Applied Mathematics 141 (2002) 5764
www.elsevier.com/locate/cam
Eigenvalue intervals for a two-point boundary
value problem on a measure chain
Douglas R. Anderson
Department of Mathematics and Computer Science, Concordia College, Moorhead, MN 56562, USA
Received 20 August 2000; received in revised form 6 December 2000
Abstract
We study the existence of eigenvalue intervals for the second-order di erential equation on a measure chain, x (t) +
p(t)f(x (t)) = 0; t [t1; t2]; satisfying the boundary conditions x(t1)-ÿx (t1) = 0 and x( (t2))+ x ( (t2)) = 0, where
f is a positive function and p a nonnegative function that is allowed to vanish on some subintervals of [t1; (t2)] of the
measure chain. The methods involve applications of a ÿxed point theorem for operators on a cone in a Banach space.
c 2002 Elsevier Science B.V. All rights reserved.
MSC: 34B99; 39A10; 39A99
Keywords: Fixed point theorems; Green's function
1. Introduction
One goal as the result of Hilger's [18] initial paper introducing measure chains has been the
uniÿcation of the continuous and discrete calculus, and then extending those results to di erential
equations on time scales. Some other early papers in this area include Agarwal and Bohner [1],
Aulbach and Hilger [6] and Erbe and Hilger [12].
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