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

Basant Karna and Bonita A. Lawrence

 Department of Mathematics, Marshall University, Huntington 25755, WV, USA
Received 31 January 2006; Revised 15 April 2006; Accepted 19 April 2006

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.