Oscillation for Forced Second-Order Impulsive Nonlinear Dynamic Equations on Time Scales

Mugen Huang,Kunwen Wen

doi:10.1155/2019/7524743

Abstract

As the unification and development of impulsive differential equations and difference equations, impulsive dynamic equations on time scales are a powerful tool to simulate the natural and social phenomena. In this paper, we study the interval oscillation of a type of forced second-order nonlinear impulsive dynamic equations with changing signs coefficients. By using the Riccati transformation technique, we obtain some new interval oscillation criteria, based only on information of a sequence of subintervals of positive axis. In addition, we provide an example to illustrate the use of our oscillatory results.

Highlights

To unify continuous and discrete dynamics in a synthetical theory, Hilger introduced the theory of time scales in 1990 [1], which provides a powerful tool to study some traditionally separated fields in an uniform model [2, 3]
We study the interval oscillation of a type of forced second-order nonlinear impulsive dynamic equations with changing signs coefficients
As an adequate mathematical tool to model the natural and social phenomena observed in physics, chemistry, biology, economics, neural networks, and social sciences, the topic is in spotlight with significant implications and has been a hot area of research for several years [4,5,6,7]

Summary

Introduction

To unify continuous and discrete dynamics in a synthetical theory, Hilger introduced the theory of time scales in 1990 [1], which provides a powerful tool to study some traditionally separated fields in an uniform model [2, 3]. We study the interval oscillation of a type of forced second-order nonlinear impulsive dynamic equations with changing signs coefficients. Anderson and Zafer [5] established interval oscillation criteria for second-order super-half-linear functional dynamic equations with delay and advance arguments.

Results

Conclusion