具有滞后和超前泛函微分方程拟线性化方法

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3、?1ïÄ,ÏLES,/ÏAscoli-Arzela½n,Bellmanت,)%CS²•9pÂñ(J.'…c¢‘‡c‘[‚5z•{²•ÂñpÂñIAbstractAbstractWiththeincreasingdevelopmentofnaturalscience,inthefieldofnaturalscienceincludingphysics,theoryofcontrol,biology,medicine,economiesandedgingfield,manymathematicalmodelswhicharedescribedbydiffe

4、rentialequationsareproposed.Differentialequationsarepowerfultoolsthatdescribethelawofnature,butitisdifficulttofindtheirgeneralsolutions.Therefore,therehasbeenanincreasinginterestinthestudyofthenatureofsolutionsofdiffer-entialequationintheory.Thispaperwillusemonotoneiterativetechniquetoresea

5、rchfunctionaldifferentialsystemswithretardationandanticipation.Thisdissertationfocusesontwosides:oneisthebasictheoryoffunctionaldifferentialsystemswithretardationandanticipation,theotheristheconvergencetheoryoffunctionaldifferentialsystems.Thepaperismadeupoftwochapters.Inchapterone,wegive

6、asurveytothedevelopmentandcurrentstateoffunctionaldifferentialsystemswithretardationandanticipation,aswellasthemainworkstatus.Inchaptertwo,Aclassoffunctionaldifferentialsystemsrelativetobothretardationandanticipationisinvestigated.Byusingmonotoneiterativetechnique,Ascoli-ArzelatheoryandBe

7、llmaninequality,constructingmonotonesequences,obtainquadraticandrapidconvergenceofthesequences.KeywordsRetardationAnticipationQuasilinearizationMethodQuadraticConver-genceRapidConvergenceII11ÙXØ11ÙXØ1.1‘‘‘KKK555Cc5,‘XêÆ3gÄ››!)ÔêÆ!ÏÕnØ9OŽÅäEâg,‰Æ†>‰Æ+•2•A^,3éõ¢S¯K¥JÑŒþž¢ÄåXÚêÆ.,ž¢´•*

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