泛函微分方程的線性化全局吸引性及臨界振動(dòng)性.pdf

1、湖南大學(xué)博士學(xué)位論文泛函微分方程的線性化全局吸引性及臨界振動(dòng)性姓名：唐先華申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：庚建設(shè)2000.2.1ABSTRACTInthispaper，wegivethedetailedanalysisoftheglobalexistenceandglobalattractivityofsolutionsofthreefunctionaldifferentialequationswhichcontainmany

2、ecologicalmodelsz’(t)【1z(t)][1ez(t)]F(t，z())=0，。7(t)[1。(t)】[1一c￡(t)]F(t，z())=0andz7(￡)[1z(t)】F(￡，(1A。())z())=0，andthe3／2globalattractivityresultsaxeobtainedbymeansoftheconditionsofat—tractivityofthelinearizeequationsofth

3、eabove；Byestabfishingtheequivalenceforoscillationofdelayandordinarydifferenialequations，weinvestigatetheoscillatorybehaviorofthefollowingfirstorderdelaydifferentialequationz訛)p(t)。(r(≠))=0，t≥tointhecriticalstatenthneutra

4、ldelaydifferentialequationwith“integrallysmall’’coe伍cients【2(t)一P(￡)2(t—r)]恤)Q(t)z(￡一口)=0，t≥toandthefirstorderneutraldelaydifferentialequationwithpositiveandnegativecoef丘cients【∞(t)一R(t)zO—r)】7P(t)z(t—f)一q(t)z(t—a)=0，t≥t

5、oweobtainmanynewresultsonoscillationandnonoscillationofsolutionsfortheaboveequationsOfthem，manyresultsare“bestpossible’’insomesenseKeywords：delaydifferentialequation，linearize，globalattractivityoscillation，criticalstate2