 
Summary: MULTIPLE PERIODIC SOLUTIONS FOR A SECONDORDER
PROBLEM ON PERIODIC TIME SCALES
DOUGLAS R. ANDERSON
Abstract. Green's function for a secondorder delta dynamic equation is
found, then used as the kernel in an integral operator to guarantee the exis
tence of positive periodic solutions to a secondorder periodic boundary value
problem with periodic coefficient functions.
1. Introduction to the Periodic Problem
Throughout this work we assume a working knowledge of time scales and time
scale notation; please see Hilger [1], Agarwal and Bohner [2], or the recent books by
Bohner and Peterson [3, 4] and Kaymak¸calan, Lakshmikantham, and Sivasundaram
[5].
Let T R, T > 0, and let T be a Tperiodic time scale; in other words, T is a
nonempty closed subset of R such that t + T T and µ(t) = µ(t + T) whenever
t T. Define the delta differential operator L by
(1) Ly(t) :=  py
(t) + q(t)y
(t), t T,
and consider the boundary value problem
(2) Ly(t) = f(t, y
