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三阶常系数拟线性泛函微分方程的周期解 被引量：3

Periodic solution of a third-order quasilinear functional differential equation with constant coefficients
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摘要 研究了一个三阶泛函微分方程周期解的存在唯一性和全局吸引性:x′′′(t)+ax′′(t)+bx′(t)+cx(t)+g(t,x(tτ))=p(t).这是一个常系数拟线性泛函微分方程.通过将这个方程转变为三维的拟线性微分方程(组),得到了这个方程存在唯一周期解的充分条件;通过选取适当的李雅普诺夫函数,推导了这个方程解的全局吸引性;进一步,得到了此方程周期解的全局吸引性.最后,举出了两个应用实例. This paper considers the existence, uniqueness and global attractivity of a periodic solution for a third-order functional differential equation：x′′′（t）＋ax′′（t）＋bx′（t）＋cx（t）＋g（t,x（tτ））=p（t）.which is a third-order quasilinear functional differential equation with constant coeffcients. By converting this equation into a three-dimensional quasilinear one, the sufficient conditions for the existence of exactly one periodic solution of this equation are established. By constructing suitable Lyapunov functionals, the global attractivity of a solution for the above equation is established; Moreover, the global attractivity of a periodic solution is established. In the last section, two examples will be provided to illustrate the applications of the results
作者 田德生
机构地区 湖北工业大学理学院
出处 《纯粹数学与应用数学》 CSCD 2013年第3期233-240,共8页 Pure and Applied Mathematics
关键词 泛函微分方程 周期解 唯一性 全局吸引性 functional differential equation, periodic solution, uniqueness, global attractivity
分类号 O175 [理学—基础数学]
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参考文献13

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共引文献8

同被引文献48

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纯粹数学与应用数学
2013年 第3期

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