Nonlinear Functional Analysis (Notes on Mathematics and It Applications)

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1、NONLINEARnotesonFUNCTIONALmathematicsANALYSISanditsapplicationsJacobTSchwartzGORDONANDBREACHSCIENCEPUBLISHERSNonlinearFunctionalAnalysisJ.T.SCHWARTZCourantInstituteofMathematicalSciencesNewYorkUniversityNotesbyH.FattoriniR.NirenbergandH.PortawithanadditionalchapterbyHermannKarcherGORDONANDBREAC

2、HSCIENCEPUBLISHERSNEWYORKLONDONPARISCopyright©1969byGORDONANDBREACHSCIENCEPUau3SHERSINC.150FifthAvenue,NewYork,N.Y.10011LibraryofCongressCatalogCardNumber:68-25643EditorialofficefortheUnitedKingdom:GordonandBreachSciencePublishersLtd.12BloomsburyWayLondonW.C.1.EditorialofficeforFrance:Gordon&Br

3、each7-9rueEmileDuboisParis14eDistributedinCanadaby:TheRyersonPress299QueenStreetWestToronto2b,OntarioAllrightsreserved.Nopartofthisbookmaybereproducedorutilizedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recording,orbyanyinformationstorageandretrievalsystem,withoutpermiss

4、ioninwritingfromthepublishers.PrintedinEastGermany.Editors'PrefaceAlargenumberofmathematicalbooksbeginaslecturenotes;but,sincemathematiciansarebusy,andsincethelaborrequiredtobringlecturenotesuptothelevelofperfectionwhichauthorsandthepublicdemandofformallypublishedbooksisveryconsiderable,itfollo

5、wsthatanevenlargernumberoflecturenotesmakethetransitiontobookformonlyaftergreatdelayornotatall.Thepresentlecturenoteseriesaimstofilltheresultinggap.Itwillconsistofreprintedlecturenotes,editedatleasttoasatisfactorylevelofcompletenessandintelligibility,thoughnotnecessarilytotheperfectionwhichisex

6、pectedofabook.Inadditiontolecturenotes,theserieswillincludevolumesofcollectedreprintsofjournalarticlesascurrentdevelop-mentsindicate,andmixedvolumesincludingbothnotesandreprints.JACOBT.SCHWARTZMAURICELEvIContentsIntroduction....................IChapter1:BasicCalculus..............9ChapterII:Har

7、dImplicitFunctionalTheorems........33ChapterIII:DegreeTheoryandApplications...:....55ChapterIV:MorseTheoryonHilbertManifolds.......99ChapterV:Category................155ChapterVI:ApplicationsofMorseTheorytoCalculusofVariationsinth