 
Summary: Thirdorder rightfocal multipoint problems on
time scales
DOUGLAS R. ANDERSON* and ALBERTO CABADA
Department of Mathematics and Computer Science, Concordia College, Moorhead, MN 56562, USA
Departamento de Ana´lise Matema´tica, Facultade de Matema´ticas, Universidade de Santiago de
Compostela, Galicia, Spain
(Received 3 May 2006; in final form 1 June 2006)
We are concerned with the existence and form of positive solutions to a thirdorder multipoint boundary
value problem on time scales with mixed derivatives. We find and utilize the Green function for the
corresponding homogeneous rightfocal problem as the kernel of an integral equation of Hammerstein
type. Two examples are included to illustrate the results.
Keywords: Boundary value problem; Time scale; Third order; Green's function
2000 Mathematics Subject Classification: 34B18; 34B27; 34B10; 39A10
1. Introduction
The theory of dynamic equations on time scales began in the literature in 1988 with the
publication of the doctoral thesis of S. Hilger [16]. The aim of this theory consists in the study of
differentialanddifferenceequationsunderthesameformulation.Thus,theconceptsofDand7
derivatives together with D and 7integrals have been defined. These two concepts cover both
