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

Impulsive periodic boundary value problems for dynamic equations on time scale

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.