无限时滞中立型泛函微分方程解的有界性

Boundedness for solution of neutral functional differential equation with infinite delay

选取空间Cg为无限时滞系统解所在的相空间,研究一类无限时滞中立型泛函微分方程解的指数渐近稳定性及有界性,运用Bellman不等式及比较原理,在适当的条件下,得到了无限时滞系统的解g-指数渐近稳定蕴涵g-有界性这一个新结论,该结论与迪申加卜在Ch空间中所得结论互不包含。

Choosing the space Cg as the phase space of the solutions for the systems with infinite delay, the exponentially asymptotic stability and the boundedness of the solutions, for a king of neutral functional differential equations with infinite delay, are investigated. By using of Bellman inequality and the comparison theorem, under some suitable conditions, the new result that the g-exponentially asymptotic stability implies the g-boundedness of the solutions is obtained. The obtained results are different from the one given by Dishen Jiabu at the phase space Ch.