The Existence And Uniqueness Of Almost Periodic Type Solutions For Several Kinds Of Evolution Equations

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.