一类具二阶非线性项的Liénard方程的定性分析及应用

Qualitative Analysis and Application on a Kind of Liénard Equations with Second Order Nonlinear Term

本文通过对一类具二阶非线性项的Liénard方程的定性分析得到了关于其解的存在性、单调性及振荡性的若干结果,并作为推论给出了具典型意义的几个非线性发展方程行波解的重要性质.这些性质不仅对于定性分析有意义,而且可使我们知道解的大致形状,从而提高求解的效率.

By qualitative analyzing a kind of Liénard equations wi th second order nonlinear term,we obtain many results of its solution,such as ex istence,monotony and oscillation.Therefore,we find important properties of trave lling wave solutions about some nonlinear equations which have representative si gnificance.These properties not only bear important meaning towards qualitative analysis,but also make us know approximate shape of their solutions so that impr ove solving efficiency.$$$$