Thispagecontainsthefollowingsections:EducationResearchInterestsClassesTaughtSomeRecentPublicationsEmploymentsProfessionalMembershipsOtherProfessionalActivitiesContactInformation

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[USU][Math/Stat][Faculty]

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EducationB.S.Mathematics,1982,JilinUniversity,ChinaM.S.Mathematics,1984,TheChineseAcademyofSciencesPh.D.Mathematics,1986,TheChineseAcademyofSciences

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EmploymentsHistory1986-1988,PostdoctoralFellowandAssistantProfessor,PekingUniversity,P.R.China1988-1989,VisitingMember,CourantInstituteofMath.Sci.,NewYorkUniversity1989-1990,VisitingAssistantProfessor,UniversityofUtah1990-1991,VisitingAssistantProfessor,UniversityofWisconsinatMadison1991-1994,AssistantProfessor,UtahStateUniversity1994-1998,AssociateProfessor,UtahStateUniversity1998-present,Professor,UtahStateUniversity

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ResearchInterestsNonlinearPartialDifferentialEquationsVariationalandTopologicalMethodsinNonlinearAnalysisHamiltonianSystems

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Classesfor2005-2006academicyearFall2005RealAnalysis(Math6210)Spring2006CalculusTechniques(Math1100)andRealAnalysis(Math6220)

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SomePublications(since1997)(completelistingfromMathSciNet)PeriodicsolutionsofevenHamiltoniansystemsonthetorus(1997),(withThomasBartsch)MathematischeZeitschrift,224,65-76.Periodicsolutionsofeven,spatiallyperiodicHamiltoniansystems(1997),(withThomasBartsch)JournalofDifferentialEquations,135,103-128.OnNeumannproblemsforsemilinearellipticequationswithcriticalnonlinearity:existenceandsymmetryofmulti-peakedsolutions(1997),(withStaniMaierandKlausSchmitt)CommunicationsinPartialDifferentialEquations,22,1493-1527.EvenHamiltoniansystemsontoriandcotangentspacesoftori(1997),(withThomasBartsch)NonlinearAnalysis,Theory,MethodsandApplications,30,4123-4134.Existence,nonexistenceandsymmetrypropertyoflocalandglobalminimizersforasemilinearellipticproblem(1998),DiscreteandContinuousDynamicalSystems,SpecialVol.2,288-302.Multiplicityforsymmetricindefinitefunctionlas:applicationstoHamiltonianandellipticsystems(1998),(withPatricioFelmer)TopologicalMethodsinNonlinearAnalysis,12,207-226.Existenceandnonexistenceof$G$-leastenergysolutionsforanonlinearNeumannproblem(1999),CalculusofVariationsandPartialDifferentialEquations,8,109-122.Existenceofmanypositivesolutionsofanellipticequationwithcriticalexponentonanannulus(1999),(withMichelWillem)ProccedingsofAmericanMathematicalSociety,127,1711-1714.Nonlinearellipticequationsonexpaningsymmetricdomains(1999),(withFlorinCatrina)JournalofDifferentialEquations,156,153-181.Existenceandsymmetryofmulti-bumpsolutionsfornonlinearSchr\"odingerequations(1999),JournalofDifferentialEquations,159,102-137.Positivesolutionsforellipticequationswithcriticalgrowthinunboundeddomains,(withM.RamosandM.Willem)Calculusofvariationsanddifferentialequations(Haifa,1998),192-199,Chapman\&Hall/CRCRes.NotesMath.,410,Chapman\&Hall/CRC,BocaRaton,FL,2000.MountainPassTheoreminOrderIntervalsandMultipleSolutionsforSemilinearEllipticDirichletProblems(2000),(withS.Li)Journald'AnalyseMath\'ematiques,81,373-396.Singularminimizationproblems(2000),(withM.Willem)JournalofDifferentialEquations,161,307-320.Morsetheorywithout(PS)conditionatisolatedvaluesandstrongresonantproblems(2000),(withN.HiranoandS.Li)CalculusofVariationsandPartialDifferentialEquations,10,223-247.OntheMorseindicesofsign-changingsolutionsfornonlinearellipticproblems(2000),(withT.BartschandK.C.Chang)MathematischeZeitschrift,233,366-384.MultiplepositivesolutionsforanonlinearSchr\"odingerequation(2000),(withT.Bartsch)Zeitschriftf\"{u}rAngewandteMathematikundPhysik,51,366-384.OntheCaffarelli-Kohn-NirenbergInequalities(2000),(withF.Catrina)ComptesRendusdesS\'eancesdel'Acad\'emiedesSciences.S\'erieI.Math\'ematique,330,437-442.Symmetricsolutionsfortheprescribedscalarcurvatureproblem(2000),(withF.Catrina)IndinnaUniversityMathematicalJournal,49,779-813.OntheexistenceofsolitonsolutionstoquasilinearSchr\"odingerequations,(withM.PoppenburgandK.Schmitt)CalculusofVariationsandPartialDifferentialEquations,,14(2002)3,329-344.OntheCaffarelli-Kohn-NirenbergInequalities:sharpconstants,existence(andnonexistence)andsymmetryofextremalfunctions,(withF.Catrina)CommunicationsonPureandAppliedMathematics,Vol.LIV(2001),229-258.Asymptoticuniquenessandexactsymmetryofk-bumpsolutionsforaclassofdegenerateellipticproblems,(withF.Catrina)DCCD,,Add.Vol.III(2001),80-88.Positiveboundstateshavingprescribedsymmetryforaclassofnonlinearellipticequationsin$R^N$,(withF.Catrina)Annalesdel'InstitutHenriPoincare-Analysenonlineaire,18(2001),157-178.GluingapproximatesolutionsofminimumtypeontheNeharimanifold,(withYanyanLi)USA-ChileWorkshoponNonlinearAnalysis,inpress.NonlinearSchr\"odingerequationswithsteeppotentialwell,(withThomasBartschandAlexanderPankov)CommunicationsinContemporaryMathematics,3(2001),1-21.SymmetryBreakingofExtremalFunctionsfortheCaffarelli-Kohn-NirenbergInequalities,(withJ.Byeon)CommunicationsinContemporaryMathematics,4(2002),457-466.Lusternik-SchnirelmantheoryinpartiallyorderedHilbertspaces,(withS.J.Li)TransactionsofAmericanMathematicalSociety,354(2002),3207-3227.SolitonSolutionsforQuasilinearSchr\"odingerEquations,(withJ.Liu)ProceedingsoftheAmericanMathematicalSociety,131(2003),441-448.SolitonSolutionsforQuasilinearSchr\"odingerEquations,II,(withJ.LiuandY.Wang)JournalofDifferentialEquations,187(2003),473-493.Standingwaveswithacriticalfrequency,(withJ.Byeon)ArchiveforRationalMechanicsandAnalysis,165(2002),295-316.Caffarelli-Kohn-Nirenberginequalitieswithremainderterms,(withM.Willem)JournalofFunctionalAnalysis,203(2003),550-568.Hardyinequalitieswithboundaryterms,(withM.Zhu),EJDEs,,Vol2003(2003),No43,p1-8.Positivesolutionstoaclassofquasilinearellipticequationson$R$,(withA.Ambrosetti),DiscreteandContinuousDynamicalSystems,9(2003),55-68.Alocalminimax-newton'smethodforfindingcriticalpointswithsymmetries,,(withJ.Zhou),SIAMJournalJournalonNumericalAnalysis,42(2004),1745-1759.OntheH\'enonequation:asymptoticprofileofgroundstates,(withJ.Byeon),,submitted.AnEfficientandStableMethodforComputingMultipleSaddlePointswithSymmetries,,(withJ.Zhou),SIAMJournalJournalonNumericalAnalysis,43(2005),891-907.SymmetryofextremalfunctionsfortheCaffarelli-Kohn-Nirenberginequalities,,(withC.-S.Lin),ProceedingsoftheAmericanMathematicalSociety,132(2004),1685-1691.Multi-bump,nodalsolutionshavingaprescribednumberofnodaldomains.I.andII.,(withZ.L.Liu),Annalesdel'InstitutHenriPoincare-Analysenonlineaire,22(2005),597-608and609-631.NonlinearSchr\"odingerequationswithvanishinganddecayingpotentials,(withA.Ambrosetti),DifferentialIntegralEquations,216(2005),78-108.NodaltypeboundstatesofSchr\"odingerequationsviainvariantsetandminimaxmethods,(withZ.L.LiuandF.vanHeerden),JournalofDifferentialEquations,214(2005),358-390.SphericalsemiclassicalstatesofacriticalfrequencyforSchr\"odingerequationswithdecayingpotentials,(withJ.Byeon),JournalofEuropeanMathematicalSociety,toappear.

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ProfessionalMembershipsAMS

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OtherProfessionalActivitiesDirector,GraduateStudyinMath&Stat,1994-1997

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ContactInformationZhi-QiangWang
DepartmentofMathematicsandStatistics
UtahStateUniversity
Logan,UT84322-4205
OfficePhone:435797-3529
Fax:435797-1822
E-Mail:zhi-qiang.wang@usu.edu

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