一类带有强迫项的二阶非线性方程周期解的分歧  

Bifurcation of periodic solutions for a class of second order nonlinear equation with the forced term

作　　者：邢慧 殷子健 XING Hui;YIN Zijian(School of Science,Xi′an Polytechnic University,Xi′an 710048,China;School of Mathematics and Statistics,Xi′an Jiaotong University,Xi′an 710049,China)

机构地区：[1]西安工程大学理学院,陕西西安710048 [2]西安交通大学数学与统计学院,陕西西安710049

出　　处：《纺织高校基础科学学报》2018年第2期186-190,共5页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金数学天元基金(11626182);西安工程大学博士科研启动基金(BS1433)

摘　　要：推广某项高压输电网任务设计中提出的二阶非线性微分方程为一类特殊类型的Liénard方程.研究这类特殊类型带有强迫项的Liénard方程周期解的分歧结构.在强迫项为正的情况下,分别得到两个重要微分方程周期解是不变号的结果.并结合Crandall-Rabinowitz分歧定理判断分歧发生的条件.在参数变化的情况下得到了该方程周期解的确切个数,且所得到的解在一条只有一个拐点的抛物型解曲线上.The second-order nonlinear differential equation of the forced form,which is presented in the design of HV power transmission network,has been generalized to a special type of Liénard equation.The bifurcation structure of periodic solutions for this special type Liénard equation with with forced is investigated.When the forced term is positive,the sign of the periodic solutions obatained is constant for two important differential equations.Combing the obtained results and Crandall-Rabinowitz bifurcation,the conditions of bifuration are judged.The exact number of of periodic solution of the equation is obtained with the changes of the parameter,and the solutions obtained are on a parabolic solution curve with only one turning point.

关 键 词：受迫的Liénard方程 周期解 Crandall-Rabinowitz分歧定理 分歧 

分 类 号：O177.91[理学—数学]