幾類高階非線性差分方程的全局行為.pdf

1、蘭州大學(xué)碩士學(xué)位論文幾類高階非線性差分方程的全局行為姓名：唐國梅申請學(xué)位級別：碩士專業(yè)：數(shù)學(xué)、應(yīng)用數(shù)學(xué)指導(dǎo)教師：李萬同20100501立皇州大學(xué)碩士學(xué)位論文AbstractInthisthesis，weinvestigatetheglobaldynamicalbehaviorofsomehigherordernonlineardifferenceequationsByusingqualitativeandstabilitytheorys

2、uperiorandinferiorlimitmethod，semicycleanalysis，convergencetheorytogetherwithsomeinequalitytechniques，wesolveorpartiallysolveaopenproblemandaconjectureproposedbyLadaseta1Atfirst，inChapter2，weconsiderthenonlineardifferenc

3、eequationz住=再p瓦瓦qxtk，n=。，1，whereP，q，，andtheinitialconditionsz一七，，XOarenonnegativerealnumbers，k∈|【2，3，’weinvestigatetheboundedness，theperiodiccharacter，theinvariantintervalandtheglobalattractivityofpositivesolutionsofthea

4、boveequationweshowthatthepositiveequilibriumofthedifferenceequationisgloballyasymptoticallystableOurresultssolvetheopenproblemproposedbyKulenovidandLadasSecondlyweconsiderthedifferenceequationXnl2pxn—Xn一七q——Xnk，n=0，1，whe

5、reP，qarepositiverealnumbersandtheinitialconditionsz一是，zoarenonnegativerealnumbersWeinvestigatetheperiodiccharacter，theinvariantintervalandtheglobalattractivityofpositivesolutionsofthedifferenceequationWeshowthattheunique

6、positiveequilibriumoftheequationisaglobalattractorwithabasinthatdependsoncertainconditionsposedonthecoefficientsFinallyweinvestigatetheboundedness，theperiodiccharacter，theinvariantintervalsandtheglobalattractivityofposit