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1、VolterraIntegralandDifferentialEquationsThisisVolume167inMATHEMATICSINSCIENCEANDENGINEERINGASeriesofMonographsandTextbooksEditedbyRICHARDBELLMAN,UniversityofSouthernCaliforniaThecompletelistingofbooksinthisseriesisavailablefromthePublisheruponrequest.
2、VolterraIntegralandDifferentialEquationsT.A.BURTONDepartmentofMathematicsSouthernIllinoisUniversityatCarbondaleCarbondale.Illinois1983ACADEMICPRESSASubsidiaryofHarcoiwtBrwrJowrovich.Pithlishrr-sNewYorkLondonParisSanDiegoSanFranciscoSloPauloSydneyTokyo
3、TorontoCOPYRIGHT@1983,BYACADEMICPRESS,INC.ALLRlQHTSRESERVED.NOPARTOFTHISPUBLICATIONMAYBEREPRODUCEDORTRANSMlTlTDINANYFORMORBYANYMEANS,ELECTRONICORMECHANICAL,INCLUDINGPHOTOCOPY,RECORDING,ORANYINFORMATIONSTORAGEANDRETRIEVALSYSTEM,WITHOUTPERMISSIONINWRITI
4、NGFROMTHEPUBLISHER.ACADEMICPRESS,INC.111FifthAvenue,NewYork,NewYork10003UnitedKingdomEditionpublishedbyACADEMICPRESS,INC.(LONDON)LTD.24/28OvalRoad,LondonNW17DXLibraryofCongressCataloginginPublicationDataBurton,T.A.(TheodoreAllen),DateVolterraintegrala
5、nddifferentialequations.(hathematicsinscienceandengineering;)Bibliography:p.Includesindexes.1.Volterraequations.2.Integro-differentialequations.I.Title.It.Series.QA431.8871982515.3'882-18932ISBN0-12-147380-5PRINTEDINTHEUNITEDSTATESOFAMERICA83848586981
6、654321ContentsPrefaceix0.IntroductionandOverview0.I.StatementofPurposeI0.2.AnOverview21.TheGeneralProblemsI.I.Introduction5I.2.RelationsbetweenDifferentialandIntegralEquations7I.3.AGlanceatInitialConditionsandExistence12I.4.BuildingtheIntuition14I.5.R
7、educibleEquations182.LinearEquations2.1.ExistenceTheory222.2.LinearProperties262.3.ConvolutionandtheLaplaceTransform282.4.Stability332.5.LiapunovFunctionalsandSmallKernels312.6.UniformAsymptoticStability462.7.ReducibleEquationsRevisited582.8.TheResolv
8、ent61VviContents3.ExistenceProperties3.1.Definitions,Background,andReview663.2.ExistenceandUniqueness733.3.ContinuationofSolutions783.4.ContinuityofSolutions894.History,Examples,andMotivation4.0.Introduction974.1.VolterraandMathematicalBiology
