二阶非线性微分方程零解的全局渐近稳定性

关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令人满意的成果,但是尚嫌不足的,是这些成果多为含1,2个非线性项,3个的很少,4个的更少。本文所研究的是具有4个非线性项的问题。去掉要求Liapunov函数无穷大这个较强的条件,代之系统正半轨的有界性。正半轨线有界性的证明,是采用定性理论中构造Poin-care-Bendixson环域外境界线的方法。所得结果,比至今所见到的文献中的条件都弱。

GLOBAL ASYMPTOTIC STABILITY OF ZERO SOLUTION OF NONLINEAR DIFFERENTIAL EQUATIONS OF SECOND ORDER

In contrast with most results obtained by other authors , this paper deals with the differential systems involving four nonlinear items . By use of themethod of constructing the outer bounder of Poincare__ Bendixson region ,a theorem is proved for the global asymptotic stability of zero solution . The conditions in the theorem are much weaker than those given by other authors.