半線性及非線性微分方程的概周期型解.pdf

1、哈爾濱理工大學碩士學位論文半線性及非線性微分方程的概周期型解姓名：嚴星申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：姚慧麗20090301哈爾濱理工大學理學碩士學位論文AlmostPeriodicTypeSolutionsforSemilinearandNonlinearDifferentialEquationsAbstractOneofthemostfundamentalandimportantproblemsindifferential

2、equationtheoryisthesolutions’propertiesofdifferentialequations，theexistenceofperiodicandalmostperiodictypesolutionsforsystemshasmoreimportantsignificanceintheoryandvalueinapplicationThetheoryofalmostperiodicfunctionsandt

3、hetheoryofasymptoticallyalmostperiodicweaklyalmostperiodicandpseudoalmostperiodicfunctionswhoarederivatedbythetheoryofalmostperiodicfunctionsconstructthetheoryofalmostperiodictypefunctionsThetheoryofalmostperiodictypefun

4、ctionsplaysanimportantroleindifferentialequations，integralequationsanddifferenceequations，theasymptoticallyalmostperiodicandpseudoalmostperiodicfunctionstosomeclassesofsemilinearandnonlineardifferentialequationsaremainly

5、appliedinthispapertheexistenceofasymptoticallyalmostperiodicsolutionsandpseudoalmostperiodicsolutionstosomeclassesofsemilinearandnonlineardifferentialequationsisdiscussedTwoaspectsofthejobaremainlydidinthispaper：thefrist

6、thecompositionprombleoftheasymptoticallyalmostperiodicfunctionsisobtainedthroughtheothermethodThesecond，theexistenceofalmostperiodictypesolutionsonsomeclassesofsemilinearandnonlineardifferentialequationsisdiscussedThespe

7、cificalcontentasfollows：Firstlythecompositionprombleoftheasymptoticallyalmostperiodicfunctionshasbeenprovedinsomepapersbythepropertiesofasymptoticallyalmostperiodicfunctions，theresultisprovedbythedefinitionoftheasymptoti

8、callyalmostperiodicfunctionsinthispaperSecondlytheexistenceofmildasymptoticallyalmostperiodicsolutionononekindofsemilineardifferentialequationsisdiscussdbythepropertiesofasymp—toticallyalmostperiodicfunctionsandthecontra