Oscillation Analysis Of Several Kinds Of Differential Equations With Damping

With the increasing development of science and technology, many scientific fields have aroused the interest of mathematical researchers of the differential equations and related problems. We know that the oscillation theory of differential equations is an important and necessary part of the theory of differential equations. For many years,many scholars have carried out the exploration and Discussion on the oscillation of the differential equations. Constantly refresh people’s understanding of the differential equation, and constantly improve and promote the known conclusions. The oscillation theory of differential equations has been developing vigorously. This has the theoretical significance and the useful value. In this paper, we discuss the oscillation of several kinds of differential equations by using the generalized Riccati transform,H function and integral inequality, and get some new conclusions.The present paper is assembled as follows:Chapter 1, Introduction. We review the historical background and development trend of the theory of differential equations, and introduces the basic concepts related to this thesis, summarizes the main contents of the paper.Chapter 2, Discuss a type of second order differential equation with damping term.By using generalized Riccati transform, integral inequality and average function. We obtain some sufficient conditions for the oscillation of the equation.Chapter 3, Discuss a type of second order differential equation with damping term.By using generalized Riccati transform, integral inequality and average function. We obtain some sufficient conditions for the oscillation of the equation.Chapter 4, Given the oscillation criteria for a class of three order nonlinear neutral differential equations. Our results improve and generalize some results in the literature.