幾類微分方程Hyers-Ulam穩(wěn)定性問題的研究.pdf

1、獨創(chuàng)性聲明本人聲明所呈交的學位論文是本人在導(dǎo)師指導(dǎo)下進行的研究工作及取得的研究成果據(jù)我所知，除了文中特別加以標注和致謝的地方外，論文中不包含其他人已經(jīng)發(fā)表或撰寫過的研究成果，也不包含為獲得安徽大學或其他教育機構(gòu)的學位或證書而使用過的材料與我一同工作的同志對本研究所做的任何貢獻均已在論文中作了明確的說明并表示謝意學位論文作者簽名：須殂南簽字日期：夕Df湃上與歹7同學位論文版權(quán)使用授權(quán)書本學位論文作者完全了解安徽大學有關(guān)保留、使用學位論文的

2、規(guī)定，有權(quán)保留并向國家有關(guān)部門或機構(gòu)送交論文的復(fù)印件和磁盤，允許論文被查閱和借閱本人授權(quán)安徽大學可以將學位論文的全部或部分內(nèi)容編入有關(guān)數(shù)據(jù)庫進行檢索，可以采用影Ep、縮印或掃描等復(fù)制手段保存、匯編學位論文學位勰囂翻棚榔’名：劣她建學位論文作者簽名：殂丑_1缸導(dǎo)師簽名：／／磐炒筆年邏～簽字日期：j口／辟玉月j7日簽字日期：勁兒年芏月習日ABSTRACTTheresearchofHyers—Ulamstabilitystemsfromthe

3、generalfunctionalequationsproposedbySUIam：whenisittruethataapproximatesolutionofgivenequationmusthaveaprecisesolutionnearbyDHersusedthedirectmethodandsolvedpartofUlam’SproblemintheframeworkofBanachspaceTRassiasintroduced

4、theconceptofunboundedCauchydifferenceandextendedtheHyers’StheoremtothecaseofapproximatelinearmappingsAfterthat，suchproblemswerecalledHyers—Ulamstabilityproblem，whichattractedalotofmathematiciansattentionManyanimportantre

5、sultisobtainedForinstanceSJungstudiedtheHyers—UlamstabilityoftheJensenfunctionalequationsandthefirstorderlineardifferentialequationsThispapermainlystudiestheproblemofHyersUlamstabilityoftheintegerorderdifferentialequatio

6、nsandfractionalorderpartialdifferentialequationsThemaincontentofthisthesisisarrangedasfollows：Inthefirstchapter，wefirstintroducebrieflytotherealitybackgroundandthesignificanceofresearchofdifferentialequationsandHyers—Ula

7、mstability，thenthispapercontentisarrangedInthesecondchapter，somepreliminaryknowledgeofneedisintroducedInthethirdchapter，wediscusstheHyers—Ulamstabilityofsecondorderconstantcoefficientdifferentialequationsandpartialdiffer

8、entialequationsInthefourthchapter，itconsiderstheHyers—Ulamstabilityoffractionaldifferentialequation，Thefirstsectionfirstlyintroducesthatfractionalordermixedpartialdiffer—entialequationsisconvertedtoasecondorderdifferenti

9、alequationbyusingfractionaltransformAndthenwediscusstheHyersUlamstabilityofthesecondorderdifferentialequation，SOtheoriginalequationisobtainedwithHyersUlamstabilityThesecondandthirdsectionswediscusstheHyersUlamstabilityof

10、fractionalorderpartialdifferentialequationsFirstly，thefractionalorderpartialdifferentialequationsisconvertedtoafirstorderpartialdifferentialequationbyusingfractionaltransformSecondly，thefirstorderpartialdifferentialequat

11、ionisconvertedtoordinarydifferentialequationbyvariabletrans—form，andwewriteasolutionofthefirstorderpartialdifferentialequationFinally，wediscusstheHyers—Ulamstabilityofthefirstorderpartialdifferentialequation，thereforethe