| In this thesis,we study the existence and uniqueness of almost periodic type solutions for three kinds of evolution equations.This thesis is divided into the following four parts:In Chapter 1,we introduce the backgrounds of the problem and the main results of this thesis.In Chapter 2,we study the existence and uniqueness of weighted pseudo anti-periodic solutions for the fractional partial difference equations in the form△αu(n)= Au(n + 1)+ f(n),n ∈Z and△αu(n)= Au(n + 1)+ f(n,u(n)),n ∈Z,where 0<α<1,A is the generator of α-resolvent sequence {Sα(n)}n∈B(X).In Chapter 3,we investigate the existence and uniqueness of asymptotically almost altomorphic solutions for the nonautonomols evolution equations u’(t)= A(t)u(t)+ f(t),t ∈R and u’(t)= A(t)u(t)+ f(t,u(t)),t∈R,where A(t)is the generator of the evolution family U(t,s).In Chapter 4,we investigate the existence and uniqueness of asymptotically almost periodic solutions for the autonomous evolution equations u’(t)= Au(t)+ f(t),t ∈R+and u’(t)=Au(t)+f(t,u(t)),t∈R+,where A is the infinitesimal generator of C0-semigroup T(t)on Banach space X. |
