三阶常系数拟线性泛函微分方程的周期解

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.

Periodic solution of a third-order quasilinear functional differential equation with constant coefficients

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