一类具有延迟中立型微分方程的渐近概自守温和解

Asymptotically Almost Automorphic Mild Solutions for a Class of Neutral Differential Equations with Delay

各类微分方程是基于不同实际问题而建立的数学模型,研究方程的各种解的存在问题引起了国内外数学学者的关注。利用Banach压缩映射原理、概自守型函数的有关理论以及卷积族的指数二分性,针对一类具有延迟的中立型微分方程的渐近概自守温和解的存在唯一性问题进行研究。渐近概自守温和解比概自守温和解更具有一般性,因此本文所研究问题会使这类方程的应用范围更加广泛。

All kinds of differential equations as mathematical models have been built up due to different practical problems,so the problem of studying the existence of various solutions has attracted the attention of mathematical scholars at home and abroad.The problem on the existence and uniqueness of asymptotically almost automorphic mild solutions for a class of neutral differential equations with delay are researched by using Banach compression mapping principle,related theorems of almost automorphic type functions and the exponential dichotomy of convolution family in this paper.Asymptotically almost automorphic mild solutions are more general than almost automorphic mild solutions,so the research of this paper will make the scope of application on this kind of differential equations more extensive.