有首次积分的K型单调系统  

Type K Monotone Systems with a First Iategral

作　　者：胡适耕[1] 

机构地区：[1]华中理工大学

出　　处：《应用数学》1990年第2期54-58,共5页Mathematica Applicata

摘　　要：本文考察Smith[7]意义上的K型单调系统=F(χ)的渐近性质.在假定系统无闭轨且F有一个具有一定单调性质的首次积分的条件下,我们证明了,这类系统在一定区域内的解或者收敛于某一平衡点,或者对于充分大的(?)离开该区域的任一紧子集.In this paper, we investigate the asymptotic behavior of type K monotone systems x=F(x) in the sense of Smith [7]. Under the assumptions that such a system has no closed orbits and F possesses a first integral having certain monotonicity property, we prove that any solution of the system, in certain region, either converges to an equilibrium or leaves any compact subset of the region for sufficiently large time t.

关 键 词：K型单调系统 平衡点 保序同■ 

分 类 号：O175[理学—数学]