Advances in Difference Equations
Volume 2006 (2006), Article ID 63208, 8 pages
doi:10.1155/ADE/2006/63208
An existence result for a multipoint boundary value problem on a time scale
Department of Mathematics, Marshall University, Huntington 25755, WV, USA
Received 31 January 2006; Revised 15 April 2006; Accepted 19 April 2006
Copyright © 2006 Basant Karna and Bonita A. Lawrence. 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 will expand the scope of application of a fixed
point theorem due to Krasnosel'skiĭ and Zabreiko to the family of
second-order dynamic equations described by uΔΔ(t)=f(uσ(t)), t∈[0,1]∩T, with multipoint boundary conditions u(0)=0, u(σ2(1))=∑i=1nαiu(ηi), and ∑i=1nαi≤1 for the purpose of establishing existence results. We will determine sufficient conditions on our function f such that the assumptions of the fixed point theorem are satisfied,
which in return gives us the existence of solutions.