共振下n维Lienard型方程的2π周期解

本文在跨共振点条件下证明n维Lienard型方程存在2π周期解.     

EXISTENCE OF PERIODIC SOLUTION OF A NEURONIC EQUATION

１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｂｒａｉｎｏｆｍａｎｋｉｎｄｈａｓｍａｎｙｃｏｇｎｉｔｉｖｅｆｕｎｃｔｉｏｎｓｓｕｃｈａｓｌｅａｒｎｉｎｇ，ａｓｏｃｉａｔｉｏｎａｎｄｏｐｔｉｍｉｚａｔｉｏｎｅｔｃ．．Ｔｈｅｎｅｕｒｏｎｉｓｔｈｅｍｏｓｔｆｏｕｎｄａｍ...     

THE PROBLEM OF LIMIT CYCLES FOR A LIENARD TYPE CUBIC SYSTEM

The purpose of this paper is to study a general Lienard type cubic system with one antisaddle and two saddles. We give some results of the existence and uniqueness of limit cycles as well as the evolution of limit cycles around the antisaddle for system (2) in the following when parameter a1 changes.     

《同文算指》中的方程解法

《同文算指》中包括二项二次和三次方程、二次和三次一般方程、高次方程等,李之藻采用传统数学的表述方式描述西方数学的方程解法,综合中西数学说明求解方程时根的位数、次商的求法,并给出没有整数根的方程解法.从方程解法的分析发现《同文算指》是中国学者力图会通中西数学的一部数学著作.     

Liénard方程的推广及其应用

本文推广了Ｌｉéｎａｒｄ方程的类型，并用其研究了一个二次微分系统极限环的唯一性问题．     

Derivative swift-Hohenberg方程的初边值问题解的存在性

运用压缩影射原理证明了DS-H方程的初边值问题的局部解的存在性和唯一性.     

关于一类平面n+2次系统极限环唯一性的一个注记

本文继续完善文[1]和[2]的工作,利用广义Lienard方程和张芷芬唯一性定 理证明了,当n≥3时一类n+2次生化反应系统极限环的唯一性.至此,该系统极 限环唯一性问题得到完整解决.     

ON SOME PROPERTIES OF LIENARD SYSTEMS

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒａｇｅｎｅｒａｌｉｚｅｄＬｉｅｎａｒｄｓｙｓｔｅｍｓｏｆｔｈｅｆｏｒｍ ｘ=ｈ(ｙ) -Ｆ(ｘ) , ｙ=-ｇ(ｘ) ,( 1 )ｗｈｅｒｅｔｈｅｆｕｎｃｔｉｏｎｓＦ ,ｇａｎｄｈａｒｅＬｉｐｓｃｈｉｔｚｃｏｎｔｉｎｕｏｕｓａｎｄｓａｔｉｓｆｙＦ( 0 ) =ｈ( 0 ) =0 ,ｘｇ(ｘ) >0 ,　　ｘ≠ 0 . ( 2 )Ｔｈｅｒｅｈａｖｅｂｅｅｎｍａｎｙｓｔｕｄｉｅｓｆｏｒｌｏｃａｌａｎｄｇｌｏｂａｌｐｒｏｐｅｒｔｉｅｓｏｆｓｏｌｕｔｉｏｎｓｆｏｒｓｙｓｔｅｍ ( 1 ) ,ｓｅｅ[1 -9] .ＳｅｔＣ+=(ｘ,ｙ)｜ｈ(ｙ…     

一类具有偏差变元的高阶中立型Lienard方程周期解的存在性

利用重合度理论和不等式分析技巧,获得了一类具有偏差变元的高阶中立型Lienard方程(x(t)-cx(t-δ))~((m))+f(x(t))x′(t)+β(t)g(x(t-T(t)))=p(t)周期解存在性的新充分条件,推广和改进了已有文献的相关结论.     

Traveling solitary wave solutions to evolution equations with nonlinear terms of any order

Many physical phenomena in one- or higher-dimensional space can be described by nonlinear evolution equations, which can be reduced to ordinary differential equations such as the Lienard equation. Thus, to study those ordinary differential equations is of significance not only in mathematics itself, but also in physics. In this paper, a kind of explicit exact solutions to the Lienard equation is obtained. The applications of the solutions to the nonlinear RR-equation and the compound KdV-type equation are presented, which extend the results obtained in the previous literature.