| In recent years, with the development of differential equations, more and more people are interested in the oscillation and non oscillation of differential equations;see, for instance. The oscillation theory of solutions of differential equations is an important branch of the qualitative theory of differential equations. In many practical applications, there are some problems about the oscillation of the solutions of the equations, especially for the two order differential equations. The oscillation of ordinary differential equations is one of the properties of the solution of the equation. It is of great significance to the application of natural science and technology, and it has the function of physical background and mathematical model.We study on vibration of special function and general equations with damping terms of this article. In the second chapter and the third chapter, the Riccati transform is used in the proof process.Chapter 1 Preference, we introduce the main contents and its background of this paper.The first chapter is the introduction, which is about the development process of the oscillation of the solution of differential equations and its significance. The oscillation of the solutions of the differential equations has a certain understanding from the whole.Chapter 2 On the oscillation criteria of a special class of second-order nonlinear differential equations.In the second chapter, the oscillation of the equation for a given equation is studied:The Riccati transform proved its oscillation. The particularity of the process is that it should make full use of the special characteristics of the given function: 1> 0 and for all. These results improve and generalize the oscillation criteria in [1] and [2]. New theorems extend a number of related results reported in the literature and can be used in cases where we known theorems fails to apply.Chapter 3 Oscillation criteria for second-order differential equations with damping term.The third chapter is on the basis of literature [2] joined the damping term, making the equation :where. In the method of proof is also the use of the Riccati transform, and in the proof of the method of reference [3]. Whereis a quotient of two odd positive integers. In what follows, it is always assumed that... |
