一类非线性方程的有界性与极限环的存在性

Existence of Limit Cycles and Boundedness of a Class of Nonlinear Equations

讨论了一类非线性微分方程的性质 ,应用定性分析方法 ,给出了这类非线性系统存在单调轨线及其一切解正向有界的条件 .在此基础上 ,利用微分方程的环域定理获得了所述系统存在极限环的条件 .

This paper concerns with a class of nonlinear equations. By using qualitative analysis method certain conditions are given under which monotone orbits exist and all positive orbits are bounded. Then by using Poincare Bendixson theorem sufficient conditions for the existence of limit cycles are obtained.