Existence And Uniqueness Of Almost Automorphic Type Solutions To A Class Of Differential Equations With Finite Delay On Banach Spaces

In this paper,we discuss the existence and uniqueness of almost automorphic type integral solutions to a class of differential equations u'(t)=Au(t)+Lut+f(t,ut),t ? R with finite delay on Banach space,when A is a Hille-Yosida operator,L is a bounded linear operator,f is some kind of binary almost automorphic type function.In chapter 1,we introduce the research background and the main issues of this paper.In chapter 2,we present several definitions,properties and composition theorems of almost automorphic type function.In chapter 3,we recall the definition of integral solution,the variation of constants formula of the above equation and the spectral decomposition of phase space used in this works.In chapter 4,we establish the Bohr-Neugebauer property of equation u'(t)=Au(t)+Lut+g(t),t ? R,and prove the existences and uniqueness of almost automorphic type integral solutions of equation u'(t)=Au(t)+Lut+f(t,ut),t ? R.In chapter 5,we apply the main results to the reaction-diffusion equation problem.