Oscillation Of Emden-fowler And Euler Type Delay Dynamic Equations On Time Scales

Recently, the increasing interest of scholars in the qualitative research of dynamic equations on time scales, is due to the comprehensive application prospect of calculus theory on time scales. As the important subset of the qualitative research of dynamic equations, the study of oscillation behavior for dynamic equations have been paid extensive close attention, too. This thesis is investigated of the oscillation of several classes of Emden-Fowler and Euler type delay dynamic equations on time scales, obtained some new criteria such that all the solutions to the studied equations are oscillatory. The details of this paper are described as follows:In chapter one, we have a briefly summarize of time scales theory and the background and development of the study of dynamic equations on time scales.In chapter two, we concerned the oscillation of two classes of second-order delay dynamic equations on time scales. Section 2.1, we considered a generalized neutral Emden-Fowler dynamic equation on time scales, by using Riccati transformation and inequality technique, some oscillation criteria are established, which allow the neutral coefficient on more widely interval, extend and improve some known results. Section 2.2, we researched a neutral delay dynamic equation on time scales with mixed neutral term, applying Riccati transformation and various inequality technique, some new oscillation criteria are presented.In chapter three, we investigated a third-order neutral Emden-Fowler delay dynamic equation on time scales, from Riccati transformation technique and new comparison methods, obtained some sufficient conditions, such that all the solutions of equation oscillation only.In chapter four, we concerned a higher order neutral Emden-Fowler delay dynamic equation on time scales, by applying various property of time scales, Riccati transformation and comparison theorem, some new oscillation criteria are established, which extend and supplement those reported in literatures.In chapter five, we studied the oscillation behavior of an Euler type dynamic equation on time scales with p-Laplacian like operator, by using new Riccati transformation and inequality technique, some new criteria are established, which complement and improve related contributions results.In chapter six, we have the main results are introduced and summarized, and the future research tendency is prospected.