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1、QualitativeAnalysisofNonlinearEllipticPartialDifferentialEquationsVicent¸iuD.RădulescuQualitativeAnalysisofNonlinearEllipticPartialDifferentialEquations:Monotonicity,Analytic,andVariationalMethodsContemporaryMathematicsandItsApplications,Volume6QualitativeAnalysisofNonlinearEllipticPartialDifferen
2、tialEquations:Monotonicity,Analytic,andVariationalMethodsVicent¸iuD.R˘adulescuHindawiPublishingCorporationhttp://www.hindawi.comContemporaryMathematicsandItsApplicationsSeriesEditors:RaviP.AgarwalandDonalOReganHindawiPublishingCorporation410ParkAvenue,15thFloor,#287pmb,NewYork,NY10022,USANasrCityFr
3、eeZone,Cairo11816,EgyptFax:+1-866-HINDAWI(USAToll-Free)©2008HindawiPublishingCorporationAllrightsreserved.Nopartofthematerialprotectedbythiscopyrightnoticemaybereproducedorutilizedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recording,oranyinformationstorageandretrievalsystem,
4、withoutwrittenpermissionfromthepublisher.ISBN978-977-454-039-4DedicationDedicatedtoMyMother,withGratitudeandLoveContentsDedicationvIntroductionixAcknowledgmentsxii1.Monotonicitymethodsforstationaryequations11.1.Generalitiesaboutthemaximumprinciple11.2.Methodofloweranduppersolutions21.3.Analternativ
5、eproofwithoutmonotoneiterations61.4.Stabilityofsolutions91.5.Extremalsolutions111.6.TheKrasnoselskiuniquenesstheorem151.7.TheBrezis-Oswaldtheorem161.8.Applicationstosublinearellipticequationsinanisotropicmedia221.9.Bibliographicalnotes302.Bifurcationproblems312.1.Introduction312.2.Abstracttheorems3
6、22.3.Abasicbifurcationtheorem352.4.Qualitativepropertiesoftheminimalsolutionnearthebifurcationpoint372.5.Bifurcationforthelogisticequationonthewholespace422.6.Bibliographicalnotes543.Nonsmoothmountainpasstheory553.1.BasicpropertiesoflocallyLipschitzfunctionals553.2.Ekelandsvariationalprinciple573.3
7、.Nonsmoothmountainpasstypetheorems613.4.Applicationsofthemountainpasstheorem763.5.CriticalpointsandcoercivenessoflocallyLipschitzfunctionalswiththestrongPalais-Smaleproperty813.6.Bibliographicalnotes884.Non
