Studies On Oscillation For One Class Superlinear Second-order Differential Equations

The oscillation of ordinary differential equation is one of important branche of differential equations. With the increasing development of science and technology,there are many problems relating to differential equation derived from lots of practical applications, such as whether differential equation has a oscillatingsolution or not, and whether all of its solutions are oscillatory or not. Because all the structures of its emergence have deep physical background and realistic mathematical models. Many scholars take on the research of this field, they have achieved many good results. With the increasing development of scienceand technology, there are many problems relating to differential equation derived from lots of real applications and practice, such as whether differentialequation has a oscillating solution or not, and whether all of its solutions are oscillatory or not. In very resent years, great changes of this field have taken place. Especially, the second order superlinear differential equation has been paid more attentions and investigated in various classes by using different methods(see [1]-[38]).The present paper employs a generalized Riccati transformation, Integral average technique and the monotone of functions to investigate the oscillation criteria for some class of superlinear differential equations, the results of which generalized and improved some known oscillation criteria.The thesis is divided into there sections according to contents.In Chapter 1, Preface, we introduce the main contents of this paper.In Chapter 2, we study the oscillation of the second-order nonlinear damped differential equation,we mainly employed a generalized Riccati transformation and Integral average technique shallfurther the investigation and improve the main results of Xu [12], we obtained several new oscillation criteria at the end of this section.In Chapter 3, the chapter is to investigate the oscillation criteria for some class the forced second-order nonlinear damped differential equation,We mainly employed average function H^v+1(t, s)∈C(D, R), in the study of oscillatory properties differential equation (3.1.1). We obtained several new oscillation criteria at the end of this paper.