发展方程周期解

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1、ElectronicJournalofDifferentialEquations,Monogrpah03,2002.ISSN:1072-6691.URL:http://ejde.math.swt.eduorhttp://ejde.math.unt.eduftpejde.math.swt.edu(login:ftp)PeriodicsolutionsforevolutionequationsMihaiBostanAbstractWestudytheexistenceanduniquenessofpe

2、riodicsolutionsforevolu-tionequations.Firstweanalyzetheone-dimensionalcase.Thenforarbi-trarydimensions(niteornot),weconsiderlinearsymmetricoperators.Wealsoprovethesameresultsfornon-linearsub-dierentialoperatorsA=@'where'isconvex.Contents1Introduction

3、12Periodicsolutionsforonedimensionalevolutionequations22.1Uniqueness..............................22.2Existence...............................52.3Sub(super)-periodicsolutions....................103PeriodicsolutionsforevolutionequationsonHilbertspaces16

4、3.1Uniqueness..............................173.2Existence...............................173.3Periodicsolutionsfortheheatequation..............313.4Non-linearcase............................341IntroductionManytheoreticalandnumericalstudiesinappliedmathe

5、maticsfocusonperma-nentregimesforordinaryorpartialdierentialequations.Themainpurposeofthispaperistoestablishexistenceanduniquenessresultsforperiodicsolutionsinthegeneralframeworkofevolutionequations,x0(t)+Ax(t)=f(t);t2R;(1)MathematicsSubjectClassica

6、tions:34B05,34G10,34G20.Keywords:maximalmonotoneoperators,evolutionequations,Hille-Yosida'stheory.c2002SouthwestTexasStateUniversity.SubmittedMay14,2002.PublishedAugust23,2002.12Periodicsolutionsforevolutionequationsbyusingthepenalizationmethod.Notetha

7、tinthelinearcaseanecessaryconditionfortheexistenceisZT1hfi:=f(t)dt2Range(A):(2)T0Unfortunately,thisconditionisnotalwayssucientforexistence;seetheexam-pleoftheorthogonalrotationofR2.Nevertheless,thecondition(2)issucientinthesymmetriccase.Thekeypointco

8、nsistsofconsideringrsttheperturbedequationx(t)+x0(t)+Ax(t)=f(t);t2R;where>0.ByusingtheBanach'sxedpointtheoremwededucetheexistenceanduniquenessoftheperiodicsolutionsx;>0.Undertheassumption(2),inthelinearsymmetriccaseweshowthat(x)isa