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Third-order right-focal multi-point problems on time scales
 

Summary: Third-order right-focal multi-point 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 third-order multi-point boundary-
value problem on time scales with mixed derivatives. We find and utilize the Green function for the
corresponding homogeneous right-focal 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,theconceptsofD-and7-
derivatives together with D- and 7-integrals have been defined. These two concepts cover both

  

Source: Anderson, Douglas R. - Department of Mathematics and Computer Science, Concordia College

 

Collections: Mathematics