Bounded Solutions On Two Different Functional Differential Equations

In this thesis,composition theorem of weighted pseudo periodic functions and weight-ed almost automorphic functions are first proved in Stepanov sense.And then,based upon theoreis of strongly continuous operator semigroup,evolution systems and above compi-sition theorems,existence and uniqueness of bounded solutions such an weighted pseudo almost periodic solutions,weighted almost automorphic solutions on two different func-tional differential equations is investigated with Stepanov-like nonlinear term.We recall the second chapter,the third chapter,the fourth chapter.The second chapter,we recall some notations and basic knowledgels.The third chapter mainly analyzes composition theorems of weighted pseudo periodic functions are first proved in Stepanov sense and the existence and uniqueness of weight-ed pseudo periodic solution to semi-linear delay differential equation with a weighted Stepanov-like pseudo periodic nonlinear term.We first established some new results on composition of Stepanov-like weighted pseudo periodic function in Stepanov sense under a uniform continuity condition with respect to Lp norm,And then,we apply the obtained results to prove the solution of the following equation u'(t) = Au(t) + f(t,ut),t ?R (1.1) where A is the infinitesimal generator of a C0-semigroup(T(t)t?0,ut?B is defined by ut(?)= u(t +?)for??[-r,0],r is a no-negative constant,and B are specified in the later.The fourth chapter mainly analyzes composition theorems of weighted pseudo almost automorphic functions are first proved in Stepanov sense and the existence and uniqueness of weighted pseudo almost automorphic solution to abstract partial neutral functional-differential equation with infinite delay under Stepanov-like nonlinear term.We first established some new results on composition of Stepanov-like weighted pseudo almost automorphic function in Stepanov sense under a uniform continuity condition with respect to LP norm,And then,we apply the obtained results to prove the solution of the following equation dt/d(u(t)+ f(t,ut)) = A(t)u(t)+g(t,ut,t?R (1.2) where A(t):D(A(t))C X?X is a family of densly defined closed linear operators on a common domain D = D(A(t)),which is independent of t,the history ut:(0,?]?X defined by ut(?)=u(t+?),belongs to some abstract phase space B defined aximatically,and f,g:R×B?X are some suitable functions.