24580.脈沖微分方程的周期解及同宿解

1、分類號Q!Z墨：!學(xué)校代碼10542密級學(xué)號2Q!!Q21QQ鰻2脈沖微分方程的周期解及同宿解PeriodicSolutionsandHomoclinicSolutionsofImpulsiveDifferentialEquations碩士生姓名：楊海田指導(dǎo)教師姓名、職稱：李建利教授學(xué)科專業(yè)：應(yīng)用數(shù)學(xué)研究方常微分方程湖南師范大學(xué)學(xué)位評定委員會辦公室二零一四年五月ABSTRACTInthisthesiswestudytheexistenc

2、eofperiodicsolutionsandhomoclinicSOlutionsforsomeclassofsecond—orderimpulsivedifferentialequationsmainlyviavariationalmethods，criticalpointandMountianPasslemma，etcThesedissertationwillmotivatethedevelopmentofqualitativet

3、heoryofimpulsivedifferentialequationsThedissertationisdividedintothreechapters，themaincontentsarefollowsInChapter1，weintroducesomeissuesarisingfromthehistoricalbackground，statusofimpulsivedifferentialequations，pointoutth

4、emainworkandinnovationswedo，InChapter2，wegivetheexistenceofnontrivialperiodicsolutionandhomoclinicsolutionofaclassofsecond—orderimpulsivedifferentialequationSincethisequationhasadisturbancevw(t，u)whichbringsaboutdifficul

5、tiesforourresearchByusingvariationalmethods，criticalpointandMountianPasslemma，weobtainasufficientconditionofthisproblemwhichpossessatleastonenonzeroperiodicsolutionandatleastonenonzerohomoclinicsolutionandthesesolutionsa

6、regeneratedbyimposesTheresultsimprovetheexistingconclusionsAtthelastofthischapter，wegivetwoexamplestoillustratethemainresultsInChapter3，westudytheexistenceofnontrivialhomoclinicsolutionofsecondorderimpulsivedifferentiale

7、quationSincethisequationhasafunctionv(t，z)=Ⅵ∽。)一％(t，z)，whichbringsaboutdifficultiesforourresearchAndimprovetheconditionoftheliterature【32]ByusingMountainPasslemma，aweakconvergenceargumentandaweakversionofLieb’Slemma，weob

8、tainthisproblemexistingatleastonenontrivialweakhomoclincsolutionButattheV2(￡，z)=0，thatistheexistingresultsTherefore，ourresultsextendsomeknownresultsAtthelastofthischapter，toillustratethefeasibifityoftheconclusion，wealsog