一类延迟积分方程的渐近概周期解

Asymptotically Almost Periodic Solutions for Some Delay Integral Equations

积分方程解的性态是积分理论中一个重要而又基本的问题.其中关于方程的周期解、概周期型解的存在性问题更是具有重要的理论意义和应用价值.已有文献中,有的延迟是常数,而有的延迟虽为函数,但对延迟做了是概周期函数的假设.本文在某些延迟积分方程的概周期解的存在性的基础上,并利用渐近概周期函数的定义和不动点理论,讨论了一类延迟是渐近概周期函数的积分方程的渐近概周期解的存在性.

As we all known,one of the most fundamental and important problems in integral theory is the research on the properties of solutions for integral equations.Among these the existence of periodic solutions and almost periodic type solutions has important theory significant and application value.In some papers,the delay is a constant.Although the delay is a function,it is an almost periodic function.In this paper,the existence of asymptotically almost periodic solutions is discussed for some integral equation with the delay which is an asymptotically almost periodic function basing on the existence of almost periodic solution for some delay integral equations and applying the definition of asymptotically almost periodic function and fixed points theorem.