非线性奇异边值问题解的存在性

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1、山东师范大学硕士学位论文ExistenceofSolutionsforSingularBoundaryValueProblemsZhuFengTheInstituteofScienceofMathematics，ShandongNormalUniversityJinan，Shandong，250014，P．R．ChinaABSTRACTSingularboundaryvalueproblems(SBVP，forshort)haveresultedfromnuclearphysics，gasdynami

2、cs，Newtonianfluidmachanics，thetheoreyofboundarylayer，non-linearopticsandSOon．From1980ssuchproblemshavereceivedagreatdealofattentionbymanyresearchers．Thereforetheybecomeanewstudyfield，andtheremanyexcellentresults。Forexample，seetheresultsofreference【1-3，5

3、—7，20，27，30]．Inrecentyears，manyboundaryvalueproblemscandescribethedeformationofanelasticbeamequilibriumstateandhavecomprehensiveapplicationinelastic-itymechanicsandengineeringphysics．Becauseeitherthefunctionorthevariableitself,whichismathematicalmodelre

4、sultedfromsomeimportantactualprob-lems，maybesingularatendpoints，thestudyofSBVPbecomesveryactive，forexample，see[2，3，19，20—23，27—30]．Sothecontentthatwestudiedhasimportantthe-oreticalandapplicablevalue．Thispaperdiscussesthetwo-pointandm-pointsingularbounda

5、ryvalueprob-lemsmoregenerally,andobtainssomeusefulresultsonthebasisofabovediscus-810nS．Therearefourchaptersinthedissertation．Inthefirstchapter，wedealwithpositivesolutionsform-pointboundary-valueproblemswithaone-dimensionalP—Laplacian：J(如(u，))’+f(t，乱)=0，

6、0

7、eproblem牡(4)(亡)=入，(￡，u(t))，0

8、lutionwhen入arbitraryvaluein(0，+Oo)thestudyofdifferentialequationscontainingparameterswithupperandlowermethod，theresultalwaygivethescopeoftheparameters，whentheparameterissmallerthanthisrange，solutionsexist，atlast，anexampleisworked