Oscillation For Several Kinds Of Delay Differential Equation

Oscillation theory of functional differential equation is an important branch of the research field of functional differential equations, which has deep back-grounds of applications. It arises in many research areas, such as biology, ecology, physiology physics and so on.In the recent years, the study of oscillation for functional differential equa-tions attracts wide attention and gains rich achievements in scientific research. In this paper, we establish oscillation criteria for these equations, which gen-eralize or improve some existing oscillation theorems. The present paper is divided into four sections.As the introductions, in Chapter 1, the background and history of os-cillatory solution problems and oscillatory for delay differential equations are briefly addressed, and the main work of this paper are given.In Chapter 2, we study the oscillatory behavior of first-order delay differ-ential equations of the form where p,τ∈C ([t0,∞), R+), R+=[0,∞),τ(t) is non-decreasing,τ(t) 0, by applying these results, we also establish some Corollary for oscillation of the second-order nonlinear differential equa-tion. we prove the correct of our Corollary.