一类广义Liénard方程周期正解的存在性  

The Existence of Positive Periodic Solutions for a Kind of Generalized Liénard Equation

作　　者：崔笑笑 程志波[1] 姚绍文[1] CUI Xiaoxiao;CHENG Zhibo;YAO Shaowen(Henan Polytechnic University (School of Mathematics and Information Science), Jiaozuo454000,China)

机构地区：[1]河南理工大学数学与信息科学学院

出　　处：《应用数学》2019年第3期699-708,共10页Mathematica Applicata

基　　金：国家自然科学基金(11501170);中国博士后基金(2016M590886)

摘　　要：本文证明一类广义Lienard方程周期正解的存在性及渐近稳定性.我们讨论的非自治函数可满足超线性条件,克服了连续定理讨论超线性条件的困难.文章的最后,我们给出两个例子和数值解以及对应的相图和时间序列图来验证我们的结论.In this paper, by application of the Manásevich-Mawhin continuation theorem, we prove the existence and asymptotic stability of positive periodic solutions for a kind of generalized Liénard equation, and the non-autonomous function satisfies superlinear condition. At last, two examples and numerical solutions(phase portraits and time series portraits) are given to verify our conclusions.

关 键 词：广义LIENARD方程 周期正解 渐近稳定性 

分 类 号：O175.12[理学—数学]