Lienard方程存在周期正解的充分必要条件  

A necessary and sufficient condition for the existence of positive periodic solutions to Lienard equations

作　　者：贾国华 陈丽娟[1] JIA Guohua;CHEN Lijuan(College of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,南京210044

出　　处：《扬州大学学报（自然科学版）》2020年第2期1-4,共4页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11271197);南京信息工程大学人才基金资助项目(2012r101).

摘　　要：研究一类Lienard方程x″(t)+f(x(t))x′(t)+α(t)xμ(t)=h(t)周期解问题,在允许方程中Li nard项的系数f(x)在x=0处有奇性且μ>1的条件下,利用重合度拓展定理获得方程存在周期正解的充分必要条件,补充和推广了已有文献中的相关结论.By using Mawhin’s continuation theorem,the problem of periodic solutions is studied for Lienard equations x″(t)+f(x(t))x′(t)+α(t)xμ(t)=h(t).In the paper,the coefficient f(x)of the Liénard term in the equation is allowed to have singularity at x=0 andμ>1.By using a continuation theorem of coincidence degree theory,a necessary and sufficient condition for the existence of positive periodic solutions to the equation is obtained.The relevant conclusions in the literature are supplemented and generalized.

关 键 词：LIENARD方程 周期解 奇性 Mawhin重合度拓展定理 

分 类 号：O175.14[理学—数学]