Weighted Asymptotic Behavior Of Solutions To Two Kinds Of Nonlinear Evolution Equations

The main aim of this paper is to investigate weighted asymptotic behavior of solutions to two nonlinear evolution equations. This paper is divided into four parts.The first chapter, we introduce the research backgrounds and the main results of this paper.The second chapter, we recall some notations, definitions and lemmas which will be used throughout this paper.The third chapter, the main aim of this part is to investigate weighted asymptotic behavior of solutions to the semilinear Integro-differential equation where α,β∈R with β> 0, α≠0 and a+β>0, A:D(A) C Xâ†'X is the generator of an immediately norm continuous Co-semilinear defined on the Banach space X, and f:R x Xâ†'X is an Sp-weighted pseudo almost automorphic function, under certain assumptions,the conclusion is obtained by combination theorems and fixed point theorem.The four chapter, the main task of this part is to investigate weighted asymptotic behavior of solutions to the Sobolev-type differential equation where A(t):D C Xâ†'X for t ∈R is a family of densely defined closed linear operator on a domain D, independent of t, and f:R×Xâ†'X is a weighted pseudo almost automorphic function and g:R x Xâ†'X is an Sp-weighted pseudo almost automorphic function, under suitable assumptions, the main results are proved by using composition theorems and fixed point theorem.