30156.hadamard流開上變分不等式解的存在性

1、Hadamard流形上變分不等式解的存在性專業(yè)名稱：應(yīng)用數(shù)學(xué)申請(qǐng)人：曹小輝指導(dǎo)教師：范江華教授論文答辯委員會(huì)揣盤啦主席：趔筵委員：聃逖鯉￡蘭絲趣俊玲廣西師范大學(xué)碩士學(xué)位論文Hadamard流形上變分不等式解的存在性SolvabilityofVariationalInequalityProblemsonHadamardmanifoldAuthor：CaoXiaohuiSupervisor：ProfFanJianghuaSpecialty：

2、AppliedMathematicsMajor：FunctionalAnalysisGrade：2011AbstractThisthesismainlydealswiththeexistenceofsolutionsforvariationalinequalitiesonunboundedclosedconvexsetsinHadamardmanifoldToensuretheexistenceofsolutionsforvariati

3、onalinequalitiesonunboundedclosedconvexsetsinlinearspace(Euclideanspace，Banachspace)，peopleposeexceptionalfamilyelementsmethod，asthemappingispseudomonotone，theexistenceofsolutionsforvariationalinequalitiesisequivalenttot

4、henonexistenceexceptionalfamilyelementsInrecentyears，peoplebe—gantostudyvariationalinequalityproblemonRiemannmanifolds，andgavecoercivityconditionguaranteetheexistenceofsolutionsforvariationalinequalitiesonunboundedclosed

5、convexsetsThereiSnoexceptionalfamilyelementsmethodresearchonthesolvabilityofvariationalinequalitiesinHadamardmanifoldsWedefineexceptionalfamilyelementsforsinglevaluedpseudomonotoneandsetvaluedKuratowskiuppersemicontinuou

6、svariationalinequalitiesrespectivelyinHadamardmanifold，usetheexceptionalfamilyelementsmethod，weobtainthecorrespondingexistenceresultsofsolutionsforvariationalinequalitiesT婦thesisisarrangedasfollowing：InChapter1，weintrodu

7、cethestudyhistoriesofvariationalinequalityandexceptionalfamilyelementdescribesomedefinitionsandlen2inasiiiHadamardmanifoldInChapter2，wefocusontheexistenceofsolutionsforpseudomonotonevariationalinequalitiesonunboundedclos

8、edconvexsetsinHadamardmanifoldW色firstintroduceitsdualvariationalinequalities，estab5shedtheequivalencebetweentheSOlutionsetofvariationalinequalityanditsdlmlvariationalinequality胍definetheexceptionalfamilyelementforpseudom

9、onotonevariationalinequalitiesonunboundedclosedconvexsetsinHadamardmanifold，provedtheequivalencebetweentheexistenceofsolutiontodualvariationalinequalityandthenonexistenceexceptionalfamilyelements，thustheexistenceofsoluti

10、onsforvariationalinequalitiesisequivalenttothenonexistenceofexceptionalfamilyelementsWeintroducesomecoercivityconditions，studytherelationsbetweenthesecoercivityconditionsandthethenonexistenceex—ceptionalfamilyelements，we