Advances in Difference Equations
Volume 2006 (2006), Article ID 43039, 13 pages
doi:10.1155/ADE/2006/43039
Existence and nonexistence of positive solutions to a right-focal boundary value problem on time scales
Department of Mathematics, Ege University, Izmir 35100, Bornova, Turkey
Received 10 October 2005; Revised 19 January 2006; Accepted 30 January 2006
Copyright © 2006 Ilkay Yaslan Karaca. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We are concerned with proving the existence of one or more than one positive solution of an n-point right-focal boundary value problem for the nonlinear dynamic equation (−1)n−1xΔn(t)=λr(t)f(t,xσ(t)). We will also obtain criteria which lead to nonexistence of positive solutions. Here the independent variable t is in a time scale. We will use fixed point theorems for operators on a Banach space.