平面自治系统极限环的存在性及解的有界性

On the Existence of Limit-Cycles and the Boundedness of Solutions for Autonomous Plane Systems

本文利用一些新的技巧建立了保证平面自治系统存在极限环及解有界的几组充分条件,并举例说明了本文的结果对某些平面自治系统极限环存在性的确定及解的有界性的判断是十分有效的.

In this paper,we use some new techniques to deal with thd existence of limit-cycles and the boundedness of solutions of autonomous plane systems and obtain some new results.Then by using these results we study in detail the existence of limit-cycles and the boundedness of solutions for a class of cubic systems. Three examples are given to illustrate that our results are very useful.