Study On Oscillation Of Two Kinds Of Delay Differential Equations

This paper mainly deals with oscillation of two kinds of delay differential equations by using ?-method.They are two different types of delay differential equations,one is time-delay advertising investment model,the other is single population model.Furthermore,the property of every non-oscillatory numerical solution is studied.In second chapter,we mainly concerns the oscillation of the time-delay advertising investment model.Firstly,we proved that its solution oscillates about equilibrium point when b?re and r?e?[(?)lnb/r-1)]>1/e are full-filled.Secondly,by using the linear?-method and one-leg ?-method,the conditions under which the numerical solution is oscillated are given.Finally,a few examples are used to illustrate our conclusions.In third chapter,we mainly concern the oscillation of the time-delay Logistic equation which is used to describe the single species population model.Firstly,we proved its solution oscillates about equilibrium point 1/b when a?>1/e.Secondly,by using the ?-method to solve the problem,the conditions under which the numerical solution is oscillated was given.Finally,a few examples were used to illustrate our conclusions.