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1、抽象泛函微分方程的权伪概自守温和解（英文）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ThetheoryofalmostautomorphywasfirstintroducedintheliteraturebyBochnerintheearliersixties,whichisanaturalgeneralizationofalmostperiodicity[1
2、],formoredetailsaboutthistopicswerefertotherecentbook[2]wheretheauthorgaveanimportantoverviewonthetheoryofalmostautomorphicfunctionsandtheirapplicationstodifferentialequations.Inthelastdecade,severalauthorsincludingEzzinbi,Goldstein,NGuerekataandothe
3、rs,haveextendedthetheoryofalmostautomorphyanditsapplicationstodifferentialequations[17].Xiao,LiangandZhang[8]postulatedanowconceptofafunctioncalledapseudoalmostautomorphicfunction,establishedexisteneeanduniquenesstheoremsofpseudoalmostautomorphicsolu
4、tionstosomesemilinearabstractdifferentialequationsandstudiedtwocompositiontheoremsaboutpseudoalmostautomorphicfunctionsaswellasasymptoticallyalmostautomorphicfunctions(Theorems2.3and2.4，[8])•Weightedpsoucloalmostautomorphicfunctionsaremoregenoralthan
5、weightedpseudoalmostperiodicfunctionswhichwereintroducedbyDiagana[911]andrecentlystudiedbyHacene,Ezzinbi[1213],Ding[l4]・Blot,Mophou,NGuerekata,Pennequin[15]andLiu[1617]havestudiedbasicpropertiesofweightedpseudoalmostautomorphicfunctionsandthenusedthe
6、seresultstostudytheexistenceanduniquenessofweightedpseudoalmostautomorphicmildsolutionstosomeabstractdifferentialequations・Motivatedbyworks[13,16,18],weconsidertheexisteneeanduniquenessoftheweightedpseudoalmostautomorphicmildsolutionofthefollowingsem
7、ilinearevolutionequationinaBanachspaceXdx(t)dt=A(t)x(t)+ddtFl(t,x(a(t)))+F2(t,x(b(t))),teR,xeWPPA(R,p),(1)whereWPAA(R,P)isthesetofallweightedpseudoalmostautomorphicfunctionsfromRtoXandthefamily{A(t),tUR}ofoperatorsinXgeneratesanexponentiallystableevo
8、lutionfam订y{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口守温和解IPreliminariesInthissection,weintroducedefinitions,notations,lemmasandpreliminaryfactswhichareusedthroughoutthiswork.WeassumethatXisaBanachspaceendowedwiththenorm?.N,RandCstandfortheset
