多值泛函微分方程的存在性和可控性.pdf

1、蘭州大學(xué)博士學(xué)位論文多值泛函微分方程的存在性和可控性姓名：常永奎申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：數(shù)學(xué)基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：李萬(wàn)同20060501AbstractMultivaluedfunctionaldifferentialequationsandintegrodifferentialequationsaleallimportantbranchinthetheoryofnonlinearanalysis，whichhavewideapplicat

2、ionsinmailyfieldssuchaqengin∞r(nóng)ing，econonfics，optimalcontrolandoptimizationtheoryTlmrefore，itissignificanttostudytheexistenceandcontrollabilityofmultivahmdfunctionaldifferentialequationsandintegrodifferentialequationsThed

3、issertationmainlydealswiththeexistenceofsecondordermultivalucdimpul—sivefunctionaldifferentialequation，existenceandcontrollabilityoffirstordermultivaiuedneutralfunctionaldifferentialequationandintegrodiflerentialequatiou

4、withinfinitedelaycontrollabilityofSobolevtypemultivaluedfunctionaldifferentialequationandintegrod—ifferntialequationwithinfinitedelayandsemilineaxmultivaluedimpulsivefunctionaldifferentialequationandintegrodiffercntialeq

5、uationwithinfinitedelayTheresultsob—taincdarepresentedasfollows：1Existenceofsecondordermultivalucdimpulsivefunctionaldifferentialequationwiththeform(p(t)v∞))’∈F(t，Yt)isdiscussedinafinitedimensionalspace酞Undersomegrowthco

6、nditionsontheimpulsivefunctions，weprovccxistencetheoremsofSOlutionsforboththeconvexandnonconvcxproblemsOurmainresultsarebascduponBohnenblust—Karlinfixedpointtheorem，Schauderfixedpointthcoremcombinedwithaselectiontheoremo

7、fBressanandColomb02Weconsidertheexistenceofmildsolutionsoffirstorderneutralmultivaluedfunctionaldifferentialequation面d【Y(t)g(^，m)]∈Ay(t)F(z，璣)andfunctionalintegrodifferentialequation岳【Y(t)9(￡，Yt)]∈Ay(￡)J：％(z，s)F(￡，軌)with

8、infinitedelayThecontrollabilityofthemultivaluedfunctionaldifferentialsystem墨[Y(t)g(tYt)】∈Ay(t)F(t，Yt)Bu(t)andfunctionalintegrodifferentialsystenl去fY(t)9(t璣)】∈Ay(t)厶％(t，s)F(t，璣)十Bu(t)withinfinitedelayisalsodiscussedWeesta

9、blishourmainresultsintheabstractphascspace8bythetheoryofanalyticsemigroupsandafixedpointtheorem，Theseresultsimprovesomeknownonesonthecorrespondingequationswithfinitedelay3ThccontrollabilityofmildsolutionsofSobolevtypemul

10、tivalucdfunctionaldiffcrentialsystem(Ey(t))’一Ay(t)∈F(t，砌十Bu(t)andfunctionaliategrodifferentialsystem(Ey(￡))’～Ay(￡)∈lo口(t，s)F(s，Y。)dsBu(￡)withinfirfitedelayisconsideredintheabstractphasespaceBSufficientconditionsaregivenf