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MULTIPLE PERIODIC SOLUTIONS FOR A SECOND-ORDER PROBLEM ON PERIODIC TIME SCALES
 

Summary: MULTIPLE PERIODIC SOLUTIONS FOR A SECOND-ORDER
PROBLEM ON PERIODIC TIME SCALES
DOUGLAS R. ANDERSON
Abstract. Green's function for a second-order 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 second-order 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 T-periodic 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

  

Source: Anderson, Douglas R. - Department of Mathematics and Computer Science, Concordia College

 

Collections: Mathematics