Oscillation for Second-Order Nonlinear Delay Dynamic Equations on Time Scales

Zhenlai Han,Tongxing Li,Shurong Sun,Chenghui Zhang

doi:10.1155/2009/756171

Abstract

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations on a time scale ; here is a quotient of odd positive integers with and real-valued positive rd-continuous functions defined on . Our results not only extend some results established by Hassan in 2008 but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation.

Highlights

The theory of time scales, which has recently received a lot of attention, was introduced by Hilger in his Ph.D
For the notation used hereinafter we refer to the section that provides some basic facts on time scales extracted from Bohner and Peterson 3
There are few results dealing with the oscillation of the solutions of delay dynamic equations on time scales 8–15

Summary

Introduction

The theory of time scales, which has recently received a lot of attention, was introduced by Hilger in his Ph.D. We refer to the last book by Bohner and Peterson 4 for advances in dynamic equations on time scales. There are few results dealing with the oscillation of the solutions of delay dynamic equations on time scales 8–15 .

Results

Conclusion