中立型泛函微分方程的周期解

ON THE PERIODIC SOLUTION OF NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

对于中立型泛函微分方程,证明了解的毕竟有界性蕴含周期解的存在性,把常微分方程中著名的Yoshizawa周期解存在定理推广到中立型泛函微分方程,然后利用所得结果给出一类产生于电力系统的中立型时滞泛函微分方程周期解存在惟一与吸引的条件。

In this paper, we prove that the ultimate boundedness of Solutions implies the existence of periodic solutions for periodic functional differential equations of neutral type, which is an extension of Yoshizawa＇s theorem on the existence of periodic solutions for ordinary differential equations to neutral functional differential equations. Then by employing the results, we obtain sufficient conditions which guarantee the unique existence and attractivity of periodic solutions for neutral functional differential equations arising from electric systems.