抽象空间中无穷时滞微分方程概自守解的存在性

Existence of Almost Automorphic Solutions of Differential Equations with Infinite Delay in Abstract Space

研究抽象空间中无穷时滞微分方程概自守解的存在性,证明了在正实轴上存在有界解蕴含存在概自守解,并给出了结论在L otka-V o lterra型方程中的应用.我们的结果推广了经典的关于非齐次线性概周期微分方程概周期解存在性的结论.

We study the existence of almost automorphic solutions of differential equations with infinite delay in abstract space. We prove that the existence of a bounded solution on R^＋ implies the existence of an almost automorhic solution and give an application to Lotka-Volterra type equation. Our result extends the classical result on the existence of almost periodic solutions for inhomegeneous linear almost periodic differential equations.