擬線性橢圓型方程與H（Ω）空間中的強共振問題.pdf

1、華南理工大學碩士學位論文擬線性橢圓型方程與H（Ω）空間中的強共振問題姓名：胡建剛申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：沈堯天20050501AbstractThispaperismainlystudiedthreetopicsThefirstistheexistenceofinfinitelymanysolutionsofthepLaplacian—likeequations；thesecondisin——finitelymanys

2、olutionsthepMeanClnvatureequationwithcriticalexponentandthethirdisthestrongresonal]ceproblemin口m)space1151thecaneofpLaplacian—likeequationsweconsiderthesituationofsubcriticalexponentgrowthWeprovethattheequationssatisfyth

3、e(PSC)conditionwhichweakerthanfPS)conditionundersomeassumptionandthenweutilizethecriticalpointtheoremofevenflmctionalprovingthattheequationshaveinfinitymanysolutionsWhilcconsideringtheinfinitelymanysolutionsthepMeancurva

4、tureequations，wefirststatethatthenumberofsingularpointsofthelimitofthePSsequenceofthefunctionalcorrespondtotheequationsiSatmostfinitelyapplyingtheconcentrationcompactnessprincipleofLions，Sotheequationssarisfythecompactne

5、ssconditioninregionwediscussedThenweutilizethecriticaIpointtheoremofevenfunctionaItoprovethattheequationshavei11一finitelymanysolutionsInthissectionweattempttotakeoffthecoe仟icientAwhichisusedtestrictthegrowthofthesubcriti

6、caltermf(x，u)insomearticles，andwestatetheconditionofrfz，u)inthissituationThispaperalsoconsiderexistenceproblemandstrongresonanceproblemofquasilinearellipticequationsintheHfQlspace訛statethebaseproblemsofH(Q)spacesuchasImb

7、eddingtheorem，compactnessofimbeddingandtheeigenvaluecharacterWecontinueourstudiedbydiscussingtheexistenceofsolutionsofequationinH(fi)，infact，wegeneralizetheclassical∽R)conditionin明(Q)spacewhichsmallerthanH(9)spaceFinally