中文摘要：

在这份报纸，我们与一条很一般的生长法律和 驾驶M 的散开 $$\frac 应付模特儿{{ \partial u ( t ， x )}}{{ \partial t }}= D\Delta ( \frac {{ u ( t ，吗 x )}}{{ M ( t ， x )}})+ \mu ( t ， x ) f ( u ( t ， x )， M ( t ， x ))为时间依赖者功能 M 的一般盒子的.$$并且????？？

英文摘要：

In this paper, we deal with the model with a very general growth law and an M- driven diffusion For the general case of time dependent functions M and #, the existence and uniqueness for positive solution is obtained. If M and # are T0-periodic functions in t, then there is an attractive positive periodic solution. Furthermore, if M and # are time-independent, then the non-constant stationary solution M（x） is globally stable. Thus, we can easily formulate the conditions deriving the above behaviors for specific population models with the logistic growth law, Gilpin-Ayala growth law and Gompertz growth law, respectively. We answer an open problem proposed by L. Korobenko and E. Braverman in [Can. Appl. Math. Quart. 17（2009） 85-104].