一類(lèi)二階微分方程有界解的討論及其應(yīng)用.pdf

1、碩士學(xué)位論又Y1531134一類(lèi)二階微分方程有界解的討論及其應(yīng)用0ntheStructureofthesetofBoundedSolutionsforaTypeofNonautonomousDifferentialEquations學(xué)科專(zhuān)業(yè)：研究生指導(dǎo)教師：基礎(chǔ)數(shù)學(xué)張麗娟李德生教授天津大學(xué)理學(xué)院二零零八年六月AbstractInthispaper，wegivesomeprecisedescriptionsofthestructurean

2、dbehaviorofboundedsolutionsfornon—autonomoussecond—orderequation：zⅣ9(z)z74f(Oth，z)=0withcompactbasespaceHanddrivingsystempincasef(Othx)isstrictlydecreasinginzonsoineinterval(n，6)Thestabilityoftheboundedsolutionswithrespe

3、cttoperturbationsinInthesecondpartofthepaper，wewilltrytoestablishsomeanalogousnewresultsfor(11)bydevelopingsomeelementarytechniquesin[9】，[10]，[13】and[15]，combiningwiththebasictheoryofpullbackattractorsforcocycledynamical

4、systemsWealsoestablishsomestabilityresultsconcerningthestructureofboundedsolu—tionsThroughoutthepaper，wewillalwaysassumetheequationsatisfiesthefollowingstructureconditions：(F1)：g(x)≥60，andg(z)isLipschitzcontinuous●(F2)：y

5、(Oth，z)iscontiniousandstrictlydecreasingwithrespecttoz(F3)：(H，d)isacompactmetricspaceHisminimal，moreover，OtH=日，ieVh，athlt∈R)=HInthethirdsectionwewilldescribeanexampleoftheabovetheoremandconclusionsAtlast，wesummarizethere