Oscillation of fourth-order dynamic equations

Abstract

In this paper we shall reduce the problem of the oscillation of all solu- tions of certain nonlinear fourth-order dynamic equations to the prob- lem of oscillation of two second-order dynamic equations, which are discussed intensively in the literature. Further oscillation criteria of fourth-order equations are given and proved using integration and Tay- lor’s formula on time scales. Some conditions are presented that ensure that all bounded solutions of the equation are oscillatory.