On Oscillation Of A Food-limited Population Model With Impulse And Delay

In the real world, impulsive phenomena exist in the procrss of many things' chang-ing or developing. In order to give a exact description of this prscess, adoptation ofimpulsive differential equations is a more effective method. Consequently, the researchson impulsive differential equations are of great theoretical or practical importance.In addition, the oscillation of impulsive differential equations is a very meaningfulsubject of research, which is important in ecological system, epidemiology and physcicsetc. Further, the oscillation of impulsive differential equations have been studied bymany author.In this thesis, we shall study the oscillation of a class of generalized food-limitedmodel with impulsive effects. (*)Chapter 1 introduces mainly the research significance and development of food-limited models.Chapter 2 gives preliminaries and lemmas that are needed in this thesis. In par-ticular, we shall reduce the oscillation the impulsive differential equation t≥T₀≥0, b_k＞-1.to the differential equation (?)(t)=-r(t)(multiply from h(t)≤t_k＜t (1+b_k)^-1)x(h(t)) (1+(multiply from T₀≤t_k＜t (1+b_k))x(t))/(1+sum from i=1 to m p_i(t)[1+(multiply from T₀≤t_k＜g_i(t) (1+b_k))x(g_i(t))])Chapter 3 obtains the sufficient conditions that guarantee the oscillation andnonoscillation of the model (*). Chapter 4 is devoted to the oscillation of the following impulsive differential equa-tionandIn addition, some results in this thesis have been published in Journal of Mathe-matical Analysis and Applications.