一类微分方程的指数增长的温和渐近概自守解

Exponentiauy Mild Asymptotically Almost Automorphic Solutions for a Class of Differential Equation

微分方程的各类解的存在问题是微分方程领域的一个重要研究方向.概自守型函数是比周期函数、概周期型函数更广的一类函数.为了研究具有指数增长的渐近概自守函数在一类带有初始条件的微分方程中的应用,依据指数增长的渐近概自守函数的定义以及C0半群的有关理论,讨论了这类方程的指数增长的温和渐近概自守解存在唯一性问题.

The existence problem of all kinds solutions for differential equation is an important study direction of differential equation field.Almost automorphic type functions are more extensive functions than periodic functions and almost periodic type functions.In order to study the applications of exponentiauy asymptotically almost automorphic function on a class of differential equation with initial condition,the existence and uniqueness problems of mild asymptotically almost automorphic solution for this kind of equation are discussed by the definition of exponentiauy asymptotically almost automorphic function and some theorems on C0-semigroup.