一类非线性微分方程组解的有界性

Boundedness for a class of non-linear differential equations

对一类著名的非线性微分方程组x.=h(y)-F(x),y.=-(x,y)k(y)+e(t)的解的有界性进行了研究,得到了该系统解的正向有界性的新的充分条件和必要条件。举例说明所获得的结果推广和改进了一些前人得出的结论。

This paper obtained necessary and sufficient conditions for the boundedness for a class of important nonlinear differential equations ：x = h （y）- F（x）,y =- （x, y）k （y）＋ e（t）. An illustrative example was given to show that the results reached by many authors are extended and improved.