不可微泛函的臨界點理論與橢圓邊值問題研究.pdf

1、同濟大學(xué)博士后學(xué)位論文不可微泛函的臨界點理論與橢圓邊值問題研究姓名：章國慶申請學(xué)位級別：博士后專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：邵嘉裕20090101ABSTRACTInthelasttwoorthreedecades，non—differentiablecriticalpointtheoryandellipticboundaryvalueproblemhavebeenstudiedextensively，becausemanyfreebound

2、aryvalueproblems，obstacleproblemsandheatdistributionproblemscanbetransformedintoellipticequation(systems)withdiscontinuoustermsTheaimofthispaperistostudytheexistenceofsolutionandmultiplesolutionsforellipticproblemswithdi

3、scontinuousterrasbynon—differentiablefunctionalscriticalpointtheoryThemainresultsarelistedinthefollowing：1TheexistenceandmultiplicityresultsforaclassoffourorderellipticequationwithnonsmoothpotentialareobtainedBasedonthen

4、on—smoothMountainPassLemma，weconsiderthefourthorderellipticproblemswhenthenonlineartermisasymptoticallylinearandprovetheexistenceofpositivesolutionFurthermore，twonontrivialsolutionsareobtainedbyusinglocallinkingfornonsmo

5、othfunctional2Usingnon—smoothcriticalpoi印thegryandamultiplicityresultbasedonlocallinking(theoriginalsmoothversionisduetOBrezisandNirenberg)，weprovetheexistenceofmultiplesolutionsforaclassofSchrOdingertypesystemswithnondi

6、fferentiabletermsinRⅣInaddition，wegivetwoexamplestoillustrateourmultiplicityresultThen，basedonanon—smoothcriticalpointtheoryforlocally‘Lipschitzfunctionals，weinvestigateaclassofstationarySchr6dingersystemswithsubcritical

7、discontinuousnonlinearitiesandlowerboundedpotentialsthatblowupatinfinityTheexistenceofnontrivialsolutionisobtained3Usingathreecriticalpointstheoremfornon—differentiablefunctionalandaSobolevembeddingresult，weestablishthee

8、xistenceofthreeradiallysymmetricsolutionsforaclassofellipticequationinvolvingtheP—LaplacianwithdiscontinuousnonlinearitiesinthewholespaceThen，usingathreecriticalpointstheoremfornon—differentiablefunctionals，weinvestigate