无限时滞非自治竞争系统的持久性

众所周知,对于有限时滞的泛函微分方程,其相空间几乎都是采用连续函数加上确界模所构成的空间;而对于无限时滞的泛函微分方程来说,不同的方程和不同的具体问题会选取不同的相空间.合适的相空间会使得问题迎刃而解,反之,会困难重重.因此选择相空间是解决问题的首要步骤.通过选取空间Cg为相空间,考察了具有无限时滞非自治竞争系统的持久性问题.进一步,得到系统持久与非持久的充分性条件.所得结果与王克3]的结果是互不包含的.

Persistence of non-autonomous competitive systems with infinite delay

It is well known that for functional differential equation with finite delay, its phase space always structured by continuous function together with supremum norm. However, for functional differential equation with infinite delay, different functions and different concrete problems make us to choose different phase spaces. It is easy to solve the problem if a moderate phase space is chosen, on the contrary, it is difficult. So, the first step of solving problem is how to choose a moderate phase space. The persistence of nonautonomous competitive systems with infinite delay is investigated by choosing space C_g as phase space. Furthermore the sufficient conditions of persistence and non-persistence of system are obtained. These results are different from ones obtianed by Wang 3], they are non-inclusive results under the different conditions.