18698.非線性系統(tǒng)無界解的存在唯一性

1、非線性系統(tǒng)無界解的存在唯一性ExistenceandUniquenessofUnboundedSolutionofUnlUenessotn0Une0notNonlinearSystem作者：袁曉晴Author：莖i壘Qgi望g)也壘望指導(dǎo)教師：夏永輝專業(yè)：應(yīng)用數(shù)學(xué)Supervisor：!魚望g壘墜i圣!壘Major：AppliedMathematics一●_____●_●●__●___________●___●_____________

2、____________________________●___●●●_________●______________________一學(xué)位：理鱟塑Degree：叢璺璺!旦!Q￡曼竺i旦旦曼旦授予單位：浙江師范大學(xué)Institute：圣墾當(dāng)i壘墜g盟Q!三望壘!旦里i∑里!曼i主YJune，2015AbstractThispaperstudiesexistenceanduniquenessofunboundedsolutionandst

3、ructuralstabilitvfornonlinearsystemwithnonuniformexponentialdichotomyanddiscussesex—istenceanduniquenessofunboundedsolutionforperturbednonautonomousimpulsivesvstemswithunboundednonlineartermsThispaperincludesfourchapters

4、Inchapterl，webrieflyintroducetheresearchbackgroundandsomelemmasofthisdissertationInchapter2，uptillnOW，manyscholarsstudiednonlinearsystemwithnonuniNrmexponentialdichotomytheorybuttheiressentialconditionsarebasedontheassum

5、ptionthatnonlineartermsatisfieslf(t，z)l≤pe∽Differentfromstandardconsideration，inthischapter，weproveexistenceanduniquenessofunboundedsolutionforthesystemwitharelativelyconservativeassumptionthatIf(t，z)|≤pTothebestoftheaut

6、hors’knowledge，thereisnelevantpaperusingnonuniformexponentialdichotomytheorytostudytheunboundedsolutionproblemofnonlinearsystemInchapter3，weproveiflinearsystem士(￡)=A(t)x(t)admitsnonuniformexponentialdichotomythennonlinea

7、rsystemisstructuralstabilityInchapter4，F(xiàn)ennerandPinto(1999)provedthatiflinearimpulsivesystemsatisfiesISconditionwithboundednonlineartermf(t，X，叩)，thenperturbednonlinearimpulsivesvstemhasauniqueboundedsolutionWhathappensif

8、f(t，z，叩)isunboundedInthischapter，weprovethatiflinearimpulsivesystemadmitsexponentialdichotomyandnonlineartermsatisfiesIf(t，z，叼)I≤∥e剛M，thenperturbednonlinearimpulsivesvstemhasauniqueunboundedsolutionIt’sworthmentioningtha