摘要
对于二阶非线性微分方程零解的全局渐近稳定性的研究有许多很好的成果,但是研究非线性项在两个以上的文章很少.本文研究具有四个非线性项的问题,而且去掉一般要求Liapunov函数具有无穷大这个较强的条件,只要求系统正半轨线有界.正半轨线有界的证明,采用定性理论中构造Poincare—Bendixson环域外境界线的方法。
There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system, which includes one or two terms, whereas few works concern with system, which includes more than two terms. In this paper, the system which includes four nonlinear terms is studied. We obtain the global asymptotic stability of zero solution and discard the condition that requires the Liapunov function trends to infinity and only require that the positive orbit be bonnded.
出处
《湖北民族学院学报（自然科学版）》
CAS
2001年第1期44-46,共3页
Journal of Hubei Minzu University(Natural Science Edition)
