微分方程边值问题正解存在性和多重性

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1、ExistenceandMultiplicityofPositiveSolutionsofBoundaryValueProblemsofDifferentialEquations200842()()Green:IABSTRACTThisthesisisconcernedwiththeexistenceandmultiplicityofpositivesolutionsofboundaryvalueproblemsforseveralclassesofdifferentialequations.

2、Thethesiscontainsfourchapters.InChapter1,thebackgroundofboundaryvalueproblemsofdifferentialequa-tionsisintroduced.Furthermore,somefixedpointtheoremsandmainresultsarealsogiven.Chapter2isconcernedwiththesingularboundaryvalueproblemsofsecondorderdifferenti

3、alequations.Underthesuitableconditions,theexistenceofsingleandtwopositivesolutionsisestablishedbyusingthetheoryoffixedpointindex.Theexistenceofpositivesolutionsofaclassofsystemsofsecondorderordi-narydifferentialequationsofthreepointboundaryvalueproblem

4、sisinvestigatedinchapter3.ByconstructingGreen’sfunctionsandanalyzingitsproperties,originalproblemsaretransferormedintointegralequations.Andthen,underthesuitableconditionswegaintheexistenceofpositivesolutions.byusingthefixedpointthe-orem.Chapter4discus

5、sesthesamesystemsofordinarydifferentialequationsasthechapter3underthedifferentboundaryvalueconditions.Byapplyingthemethodwhichissimilartoone’sofchapter3,theexistenceofpositivesolutionsisobtained.Chapter3andChapter4aimattheboundaryvalueproblemsofthesyst

6、emsofdifferentialequations.Bycouplingthedifferentialequations,theboundaryvalueproblemsaretransformedintotheexistenceofsolutionsofrelatedintegralequa-tions.Thismethodhasseldomseeninpresentiterature.Keywords:BoundaryValueProblems;PositiveSolutions;FixedP

7、ointTheo-rems.II.........................................................................IABSTRACT..................................................................II..................................................................1§1.1§1.2§1.3§2.1§

8、2.2§2.3§3.1§3.2§3.3§4.1§4.2§4.3............................................................1............................................................3............................................................5............................9......