一类有阻尼的二阶微分方程的运动周期解  

Running periodic solution of a class of second order differential equations

作　　者：赵艳菊[1] 周盛凡[1] 

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2011年第1期31-35,共5页Journal of Shanghai Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11071165)

摘　　要：考虑具有阻尼的二阶微分方程:x″+ax'+g(x)=γ,此方程描述的是类似于钟摆的振动器运动的一个模型.首先把此二阶微分方程转化为一个与它等价的系统,然后证明该系统存在上、下解;最后根据微分方程存在运动周期解的经典结果,证明了当g(x)在一个周期内是分段线性函数时,其中,这个分段线性函数,在一个周期内包括对称和非对称两种情况.该系统存在运动周期解,这也意味着与该系统等价的原一阶微分方程存在运动周期解,且该运动周期解还具有吸引其他解的性质.We consider the second order differential equation with a damping coefficient： x″＋ax′＋g（x）=γ,this equation can model the motion of oscillators like the pendulum.First,we converse the second order differential equation to a equivalent system.After that,we prove this system exists the upper and lower solution.Finally,by the classical result of differential equation possesses running periodic solution,we prove that when g（x） is a segment linear function in a period,this system possesses a running periodic sultion,where this function includes two cases,symmetric and asymmetric in a period.This means the equivalent differential equation possesses a running periodic solution,and this solution has the nature of attracting other solutions.

关 键 词：运动周期解 二阶微分方程 非对称 分段线性周期函数 

分 类 号：O175.2[理学—数学]