含權的平均曲率方程Dirichlet問題解的存在性.pdf

1、華南理工大學碩士學位論文含權的平均曲率方程Dirichlet問題解的存在性姓名：楊俊申請學位級別：碩士專業(yè)：應用數學指導教師：沈堯天20030501II華南理工大學理學碩士學位論文AbstractThispaperismainlyconcernedabouttheexistenceofanontrivialsolutionandinfinitelymanysolutionsofDirichletproblemforaweightedme

2、ancurvatureoperatorequationItdiscussestheresultsofthisequationwhenthesingulartermandthenon—singulartermofthenonlinearpartarewithallkindsofexponentgrowthWhiletheequationiswithSobolevcriticalexponentgrowthorwithSobolev—Har

3、dycriticalexponentgrowth，usingtheresultofBrizisandLiebconcerningtherelationbetweenpointwiseconvergenceoffunctionsandconvergenceofsomefunetionalswhichmeetacertainconditions，weprovethatthefunctionalsatisfiesthelocal(PS)。co

4、nditionwhenP≥2Whilethesingulartermandthenon—singulartermareallwithsubcriticalexponentgrowth，weusetheinequalityinPeterTolksdorf’Sliteratureandprovethefunctionalsatisfies(PS)cconditionwhenP1，whereCisarealnumberfora11Whente

5、stingtheMountainPassgeometrycondition，weexploitacertaintechniqueandtestifytheMountainPassgeometryconditionisalsocontentedas1P2FinallyutilizingtheMountainPassLemmasatisfying(PS)cconditionandthecriticalpointtheoremofevenfu

6、nctionalwegettheexistenceresultsofanontrivialsolutionandinfinitelymanysolutionsforthemeancurvatureoperatorequationInaditions，wediscusstheexistenceofanontrivialsolutionforasemilinearellipticequationinRⅣandtheexistenceofap

7、ositivesolutionforaauasilinearellipticequationwithregardtoNeumannboundaryconditionByusingtheMountainPassLemmawithout(PS)condition，theformerprovesthenontrix，ialsolutionfortheequationexistswhenthecompactnessconditioninthep

8、aperreferredtobeinglostThelatterturnedtheproblemoffindingthesolutionfortheequationintoacorrespondingfunctionalrestrainingminimumproblemwhentestingwhethertheminimumproblemisachieved，weuseawaydifferentfromthecommonDirichle