一类非线性微分方程组零解的全局稳定性

ON GLOBAL ASYMPTOTIC STABILITY OF THE TRIVIAL SOLUTION OF A CLASS OF SYSTEMS OF NONLINEAR DIFFERENIAL EQUATIONS

本文考虑非线性微分方程组dx/dt=ax+f(y),dy/dt=cx+dy,f(0)=0的零解的全局稳定性。得到下面的结果:如果微分方程组满足下列的条件,a) a+d<0,b)ad->0。(y≠O) 则它的零解是全局稳定的。与文[(1).p.245]的例3相比较,我们得到的结果改进了马尔金已有的结果、并且简化了证明。

We consider global asymptotic stability of the trivial solution of systems of nonlinear differential equations. We obtain the following result: The trivial solution of systems of differential equations is globally asymptotically stable if it satisfy the following conditions a) a+d>0, b) (y≠0) In comparison with example 3^([1. p. 245]), The result we got has impraved Marke's result and simplified the procedure of the proof.