原创《抽象泛函微分方程权伪概自守温和解（英文）》：本论文为您写泛函毕业论文范文和职称论文提供相关论文参考文献，可免费下载。
摘 要利用算子半群理论和Banach 不动点定理研究了一类抽象泛函微分方程权伪概自守温和解的存在唯一性,所得结论拓展了已有结果.
关键词权伪概自守；抽象泛函微分方程；指数稳定；存在唯一性
The theory of almost automorphy was first introduced in the literature by Bochner in the earlier sixties, which is a natural generalization of almost periodicity[1], for more details about this topics we refer to the recent book[2] where the author gave an important overview on the theory of almost automorphic functions and their applications to differential equations. In the last decade, several authors including Ezzinbi, Goldstein, NGuérékata and others, have extended the theory of almost automorphy and its applications to differential equations[17].
Xiao, Liang and Zhang[8] postulated a new concept of a function called a pseudoalmost automorphic function, established existence and uniqueness theorems of pseudoalmost automorphic solutions to some semilinear abstract differential equations and studied two composition theorems about pseudoalmost automorphic functions as well as asymptotically almost automorphic functions （Theorems 2.3 and 2.4, [8]）.
Weighted pseudoalmost automorphic functions are more general than weighted pseudoalmost periodic functions which were introduced by Diagana[911] and recently studied by Hacene, Ezzinbi[1213], Ding[14]. Blot, Mophou, NGuérékata, Pennequin[15] and Liu[1617] have studied basic properties of weighted pseudoalmost automorphic functions and then used these results to study the existence and uniqueness of weighted pseudoalmost automorphic mild solutions to some abstract differential equations.
Motivated by works [13,16,18], we consider the existence and uniqueness of the weighted pseudo almost automorphic mild solution of the following semilinear evolution equation in a Banach space X
dx（t）dt等于A（t）x（t）+ddtF1（t,x（a（t）））+F2（t,x（b（t）））,t∈R,x∈WPPA（R,ρ）,（1）
where WPAA（R,ρ ） is the set of all weighted pseudo almost automorphic functions from R to X and the family {A（t）,t∈R} of operators in X generates an exponentially stable evolution family {U （t, s）,t. s}.
湖南师范大学自然科学学报第38卷第5期雷国梁等：抽象泛函微分方程的权伪概自守温和解1Preliminaries
In this section, we introduce definitions, notations, lemmas and preliminary facts which are used throughout this work. We assume that X is a Banach space endowed with the norm ||·||.N, R and C stand for the sets of positive integer, real and complex numbers. We denote by B（X） the Banach space of all bounded linear operators from X to itself. BC（R, X ）（BC（R×X, X）） is the space of all bounded continuous functions from R to X（R× X to X）. L1loc（R） denote the space of locally integrable functions on R. Let U be the collection of functions （weights） ρ：R→ （0,+∞）, which are locally integrable over R with.ρ>0（a.e.）. From now, if ρ∈U and for r>0, we then set m（r,ρ）等于∫r-rρ（t）dt, U∞：等于{ρ∈U：limr→∞ m（r,ρ）等于∞}, UB：等于{ρ∈U∞： ρ is bounded and infx∈R ρ（x）>0}.
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