Oscillation Criteria for Impulsive Dynamic Equations on Time Scales

Abstract

The study of dynamic equation on a time scales goes back to its founder Stefan Hilger [16]. He aims to unify, extend and generalize ideas from discrete calculus, quantum calculus, and continuous calculus to arbitrary time scale calculus. A time scale 𝕋 is a nonempty closed subset of real numbers. When the time scale is the set of real numbers, the general results yield the results of ordinary differential equations. On the other hand, when the time scale is the set of integers, the same general results yield the results of difference equations. The new theory of the so-called ”dynamic equation” is not only unify the theories of differential equations and difference equations, but also