 
Summary: Journal of Computational and Applied Mathematics 141 (2002) 6573
www.elsevier.com/locate/cam
Existence of three positive solutions to a secondorder
boundary value problem on a measure chain
Richard I. Averya
, Douglas R. Andersonb;
a
College of Natural Sciences, Dakota State University, Madison, SD 57042, USA
b
Department of Mathematics and Computer Science, Concordia College, Moorhead, MN 56562, USA
Received 24 August 2000; received in revised form 18 December 2000
Abstract
Growth conditions are imposed on f such that the boundary value problem x (t) = f(x (t)), t [t1; t2], x(t1) 
Áx (t1) = 0 and x( (t2)) + x ( (t2)) = 0, where t1 ¡ t2 from a measure chain T, has at least three positive solutions
by way of the ÿve functionals ÿxed point theorem. c 2002 Elsevier Science B.V. All rights reserved.
MSC: 39A10; 39A99; 34B99
Keywords: Measure chains; Boundary value problem
1. Introduction
Since Hilger's [24] initial paper unifying continuous and discrete calculus, attention is being given
to di erential equations on measure chains (time scales). To facilitate this, the calculus on measure
