對一類非線性微分方程正解的分歧解法.pdf

1、湖南師范大學(xué)碩士學(xué)位論文對一類非線性微分方程正解的分歧解法姓名：李宏波申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：李亦20070501對一類非線性微分方程正解的分歧解法ABSTRACTThisthesisofMasteriscomposedoffivechapterswhichmainlystudiesacl躺ofnonlineardifferentialequationswhenthenonlinearpartoftheequation

2、shas80mespecialconditions，usingnonlinearanalysisandbifarcationtheoremwecanknowhowmanysolutionsthenonlineardifferentialequationshave狂theAchangesThenwecontinuetesearchOnthisnonlineardifferentialequationsmorehtrtherlywhenth

3、ispositivesolutionisadegeneratecriticalsolution。wecaninferanintegalformulaE(o)firstlyanditcanjudgethesolutionscurvehowtochangeit’8directioninthe(A，u)planebyit’8valuesInthefirstchapters，thethesismainlyintroducesaclassofno

4、nlineardifferentialequationsofthehistorydevelopementandtherecentdevelopmentoftheresearchinthisequationsInthesecondchaptersitmainlyintroduces璐somepreliminaryknowledgeandrelatedlemmaaboutstudyingthisclassofthenonlineardiff

5、erentialequationsInthethirdchapter，itmainlystudieswhenthenonnearpartoftheequationshassomespecialconditions，usingnonnearanalysisandbifurcationtheoremwecanknowhowmanysolutionsthenonlineardifferentialequationshaveiftheAchan

6、gesInthefourthchapter，itcontinuetesearchonthenonlineardifferentialequationsmorefurther|ywhenthispositiveso|utionisadegeneratecriticalsolution，wecaninf醯anintegalformula曰Q)firstlyanditcanjudgethesolutionsclⅡ唧howtochangeit’