Advances in Difference Equations
Volume 2009 (2009), Article ID 603271, 10 pages
doi:10.1155/2009/603271
Research Article

Impulsive Periodic Boundary Value Problems for Dynamic Equations on Time Scale

Eric R. Kaufmann

Department of Mathematics & Statistics, University of Arkansas at Little Rock, Little Rock, AR 72204, USA

Received 31 March 2009; Accepted 20 May 2009

Academic Editor: Victoria Otero-Espinar

Copyright © 2009 Eric R. Kaufmann. 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

Let 𝕋 be a periodic time scale with period p such that 0,ti,T=mp∈𝕋, i=1,2,…,n, m∈ℕ, and 0<ti<ti+1. Assume each ti is dense. Using Schaeffer's theorem, we show that the impulsive dynamic equation yΔ(t)=−a(t)yσ(t)+f(t,y(t)), t∈𝕋, y(ti+)=y(ti−)+I(ti,y(ti)), i=1,2,…,n, y(0)=y(T), where y(ti±)=lim⁡t→ti±y(t), y(ti)=y(ti−), and yΔ is the Δ-derivative on 𝕋, has a solution.