常微分方程三點邊值問題正解的存在性研究.pdf

1、目錄摘^IIIAbstractIVl1.1問題的背景與相關(guān)研究進(jìn)展11.2工作重點及本文的研究方法21.3預(yù)備知識3第二章四階邊值問題的IH解62.1引62.2相關(guān)引理62.3存在性結(jié)果92.4相關(guān)例子14第三章偶數(shù)階邊值問題的正解153.1引言153.2相關(guān)引理163.3存在性結(jié)果203.4相關(guān)例子22第四章二階脈沖邊值問題的IH解244.1244.2相關(guān)引理254.3存在性結(jié)果304.4相關(guān)例

2、子33第五章結(jié)束語34參#想35作#敞378致AbstractThethreepointboundaryvalueproblemsofdinarydifferentialequationsariseindifferentareasofappliedmathematicsphysics.Inthispaperwemainlyresearchseveralclassesofthreepointboundaryvalueproblem

3、sofdifferentialequationsbystructuringacompletelycontinuousoperatusingsomefixedpointtheemsinequalitytechniques.Finallyweobtainseveralcriteriatheemsofsolvabilityoftheboundaryvalueproblems.Thewholepaperincludesfivechapters.

4、Inthefirstchapterweoutlinethehisticalbackgroundresearchstatusoftheproblemsfmultipointboundaryvalueproblemsthemethodsinthispapergivesomedefinitionsresultswhichwillbeusedinthispaper.Inthesecondchapterwediscusstheexistenceo

5、fpositivesolutionsfaclassoffourthderdifferentialequationsinwhichnonlineartermfcontainsthesecondorderderivativeu“：uAt)=f(tut)yt))otw(0)—=0W“(0)y9z(0)=0W(l)=“i().BymeansoftheAveryPetersontheemsomesufficientconditionsareest

6、ablishedtoguaranteetheexistenceoftriplepositivesolutionsofthisproblem.Inthethirdchapterwestudytheexistenceofthepositivesolutionsftheevenderboundaryvalueproblems(—1)“W(2“)=(W)01uli)(0)=^u2i])(0)W(2)(1)=ai]u2i](tj)0imLByus