一类带积分边界条件的弹性梁微分方程边值问题正解的存在性和唯一性

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1、应用数学MATHEMATICAAPPLlCATA2O14，27(4)：858—864nceandUniquenessofMonotoneveSoOlutionsfto0ratnElIasticBeamEquationwithIntegralBoundaryConditionsWANGLiping(~莉萍)，ZHOUZongfu(f~宗福)(SchoolofMathematicalScience，AnhuiUniversity，Hefei230601，China)Abstract：Inthispaper，aclassofBVPf

2、orafourth-orderelasticbeamequationwithintegralboundaryconditionsisconcerned．Bymeansoffixedpointtheoremofgeneralizedconcaveoperators，theresultsofexistenceanduniquenessofmonotonepositivesolutionsareobtained．OneexampleisgiventOillustratetheresults．Keywords：Existenceand

3、uniqueness；Monotonepositivesolution；Fixedpointtheo—rein；Integralboundarycondition；ElasticBeamequationCLCNumber：O175．8AMS(2000)SubjectClassification：34B15Documentcode：AArticleID：1001-9847(2014)04—0858-071．IntroductiOnFourth—ordertwo—pointboundaryvalueproblemsareusefu

4、lformateriaImechanicsbe—causetheproblemsusuallycharacterizethedeformationsofanelasticbeam[]Forexample，thefollowingelasticbeamequation一f(t，H(￡)，(￡))，(1．1)togetherwithtwo—pointboundaryconditions(0)一“(1)一“(O)一(1)一0，(1．2)UI“(O)一“(1)一“(0)一(1)一0．(1．3)TheBVP(1．1)一(1．2)desc

5、ribesthedeflectionofanelasticbeamwithbothendsrigidlyfixed．Theexistenceofpositivesolutionsorotherresultofproblem(1．1)一(1．2)W8Sstudiedextensively，see[1—6]．Theexistenceofpositivesolutionsofproblem(1．1)一(1_3)wasstud—iedin[7]．Inthepreviousresearch，theboundaryconditionsof

6、elasticbeamsequationBVParerelativelysimple．InE83，theauthorstudiedmorecomplexforthefollowingfourth—order*Receiveddate：Jan8，2014Foundationitem：SupportedbytheNationalNaturalScienceFundationofChina(11071001)andtheNaturalScienceFundationofAnhuiProvince(1208085MAl3)Biogra

7、phy：WANGLiping，female，Han，Anhui，majorindifferentialequation．N0．4WANGLipingeta1．：ExistenceandUniquenessofMonotonePositiveSolutions859two—pointboundaryvalueproblemswithnonlinearboundaryconditions，f一厂(，()，“(￡))，0≤t≤1，(1)一0，(1)一g(“(1))，(1．4)1“(o)=(0)=“wheref∈C(E0，1]×R×R

8、，R)，gEC(R，R)．Problem(1．4)meansthattheleftendofthebeamisfixedandtherightendofthebeamisattachedto8bearingdevice，givenbythefunc—tiong．Theauth