幾類差分方程邊值問題的正解.pdf

1、中南大學(xué)碩士學(xué)位論文幾類差分方程邊值問題的正解姓名：游細清申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：陳海波20061101中南大學(xué)碩士學(xué)位論文ABs，nUlCTABSTRACTTherehavebeenalotofresultsonsmd如ngboundaryvalueproblemsfordifferentialequations，butratherfewachievementsondifferenceequationsHowever

2、soastomeettheneedsofnumeficalanalogue，differentialequationsaleoftentransformedintodifferenceequations，whileotherdifferenceequationsoriginateddirectlyfrompracticalproblemssuchasmedicineandphysicsEspeciallyinrecentyears，th

3、erapiddevelopmentofcomputertechnologyhasmadetheapplicationofdifferenceequationsinvolvinginmorewidenfields，andlotsofmodelsaboutboundaryvalueproblemsofdifferenceequationsalebroughtforwardandtherefomfocusedonbymanyexpertsan

4、dscholarsButaslackoftechniquesandmethodsonstudyingtheexistenceofboundaryvalueproblemsfordiscretesystems，therearefewrelevantresultsTherefom，itismeaningfulworkeitherintheoryresearchesOrinapplicationstostudyboundaryvaluepro

5、blemsfordifferenceequationsThisdissertationdiscussesmainlytheexistenceofpositivesolutionsforfourthorderdifferenceequationboundaryvalueproblems，positivesolutionsfornorderdifferenceequationboundaryvalueproblems，multiplesol

6、utionsfor2norderdifferenceequationboundaryvalueproblemsThepaperisdividedintofourchapelsmaincontentsareasfollows：Inchapterone，Weintroduceasurveytothedevelopmentofpostivesolutionsforboundaryvalueproblems，wealsosummarizemai

7、nresultsinthedissertationInchaptertwo，weexploreanewapproachbyassociatingalgebrawithfixedpointtheoryinsteadofthetraditionalmethodofcombiningGreen’Sfunctionandfixedpointtheorysomesufficientconditionsofpositivesolutionsareo