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Critical Sobolev index of a Semilinear Elliptic Equations of Second Order Existence

6npp ・ VM + is proved. References 481AnbinThProblcmesisoperimetrlquesetespacesdeSobolev. J. Diff. Geom. 1976 {(11) :575 - 598 .2 AubinThEquatioasdiffereatiellesnon】 ineairesetproblemedeYamabeconeerna * ~ tlac0u song urescahireJ. Math. Pure $ etApPI1976: (ss) l269 - 2933BrezisH,[link widoczny dla zalogowanych], Nirenber ~ L. Po ~ itivesolutionsofnonlinearellipticequationsinvolvingcritieasobolevtxponents. COmlR1. PureAPP1Math. 1983; (36) :437 - 477 .4 Talenti. G. BestconstantinSobolevinepnallty, AnnBlidjMat. . 197110l353 - 3735Ambrosetti. A. , Rabinowitz. P. . DhalvariationalmethodsinciRicalpointtheoryandapplicatlons. I. Funct. Ana1. ,[link widoczny dla zalogowanych], R93, (iI) | 340 - 38i6StampacchiaG. . Let ~ obiemedeD ~ richletpourleseqnations ~ eIIiptiquesdusecondordreacoeffientsdiscnotinus. Ann. Inst. FourierGrenobk. 1065. (I) ti5IlB9-2587Bartoip. P. , Fortnnato. D. . Benci. V. , Abstr ~ ctcriticalpointthe0 stare andapplicatiOtt $ toSOl ~ lenonliBearprobIemswithstrongresonanceatiallnity. JOarnalofNoff ~ fieafAn_1. . T. M. A. 1983,7 c9) ,[link widoczny dla zalogowanych],981 - 10128 Zhang Gongqing. Critical point theory and its turn to open 1. Shanghai Science and Technology Agency out of turnip. 1986.9Cermi. G. ,[link widoczny dla zalogowanych], Fortnnato. D. ,[link widoczny dla zalogowanych], Struwe. M. BifurcationandraultiPlicityresultsfornonli ~ f & relIipticproblemsinvolvingSobolevexponents, Ann. fnst. HeadPoincale. AnalyseNonlinair ~ 198I. (5) :341-3sO (edit Min) TheExistenceofSolutionsforSeveralSemi-LinearEllipticEquationsInvolvingCriticalSobolevExponentsYangLinYangZhihuoABSTRACTInthispaperwediscussedthepositivesolutionsforseveralsemi-linearellipticequationsinvolvingcriticalSobolevexponents. Weobtainedsomeexistenceresultyvariationalmethodsandgenus. KeyWords: variationalmethod, bestconstantforthesobolevembedding. mountainpasstheoremwithoutthe (PS) condition, genus. 49

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