Atlas: Impulsive Periodic Boundary Value Problems for Dynamic Equations on Time Scale by Eric R. Kaufmann

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Eighth Mississippi State - UAB Conference on Differential Equations & Computational Simulations
May 7-9, 2009
Department of Mathematics and Statistics, Mississippi State University
Mississippi State, MS, USA

Organizers
Mississippi State University & University of Alabama - Birmingham

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Impulsive Periodic Boundary Value Problems for Dynamic Equations on Time Scale
by
Eric R. Kaufmann
University of Arkansas at Little Rock

Let T be a periodic time scale with period p such that 0, t_i, T = mp ∈ T, i = 1, 2, ..., n, m ∈ N, and 0 < t_i < t_i+1. Assume each t_i is dense. Using Schaeffer's Theorem, we show that the impulsive dynamic equation

y^D(t) = -a(t)y^s(t)+ f ( t, y(t) ), t ∈ T,

y(t_i⁺) = y(t_i^-) + I (t_i, y(t_i) ), i = 1, 2, ..., n,

y(0) = y(T),

where y(t_i^±) = lim_{t → t_i^±} y(t), y(t_i) = y(t_i^-), and y^D is the D-derivative on T, has a solution.

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Date received: April 7, 2009