具有Hardy項(xiàng)和Hardy-Sobolev臨界指數(shù)橢圓方程解的存在性和多重性.pdf

1、西南大學(xué)碩士學(xué)位論文具有Hardy項(xiàng)和HardySobolev臨界指數(shù)橢圓方程解的存在性和多重性姓名：丁凌申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：唐春雷20070401ExistenceandmultiplicityofsolutionsforsemilinearellipticequationswithHardytermsandSobolev—Hardycriticalexponentsl一“MajorIApplicationMat

2、hematicsSpecialitylNonlinearFunctionalAnalysisSupervisorIProLTangChunLeiAuthorIDingLing($20040809)ABSTRACTThisdissertationinvestigatesaclassofsemilinearellipticequationsJ一△Ⅱ一p1昂=恒；；蘭“A，(毛u)，z∈n＼oIu(z)=0，z∈anExistenceandm

3、ultiplicityofsolutionsarestudiedbythevariationalmethodsand80meanalysistechniquesTheaboveequationshaveHardytermsandcriticalSobolevHardyexponentsWherenisauopenboundeddomaininR。Ⅳ(Ⅳ≥3)withsmoothboundary觸and0∈n，0≤蘆2，adetailed

4、analysisonthe(PS)sequenceofthevariationalfunctionaiscorrespondingtotheequationsisgivenandalocalcompactnessresultisobtainedApplyingthiscompactneesresultandtheMountainPassLemma，thisthesisprovestheexistenceandmultiplicityof

5、solutionsoftheaboveequationsSecondlythisthesisprovestheexistenceoftwopositivesolutionsbytheachievingfunctionsofthebestSobolevHardyconstant，Ekeland’SvariationalprincipleandtheMountainPassLemmaunderthefollowing∞nditi。n8：，∈

6、e(豆R，R)，t_lim0￡氣盟=o。，f當(dāng)‰簧=o，茹∈再，，i8咖decreasingw陸。齠pecttothe8econdvariableorn。n如creasinginsuitablerange，andA∈(0，A’)，whereA’01SuppoSedbyNationalNaturalScienceFoundationofChina(No10471113)，bytheTeachmgandResearchAwardProgra