Summary: Journal of Computational and Applied Mathematics 141 (2002) 5764
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
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)-˙x (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 ˙xed 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
One goal as the result of Hilger's  initial paper introducing measure chains has been the
uni˙cation 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 ,
Aulbach and Hilger  and Erbe and Hilger .