非齊次微分方程解的復振蕩和唯一性.pdf

1、分類號UDC密級編號復旦大學博士后研究工作報告王瑁工作完成日期2QQ曼生魚旦=2QQ生壘旦報告提交日期2QQ生互且復旦大學(上海)2005年6月AbstractUniquenesstheorydealswithconditionsunderwhichthereiStheuniquefunctionsatisfyinggivenhypothesesItiswellknownthatanypolynomialisdeterminedbyit

2、szeropointsexceptforanon—constantfactorHoweveritdoesnotholdfortranscendentalentirefunctionsandmeromorphicfunetionsSOitsresearchiscomplexandinterestingComplexoscillationOfdifferentialequationscontainstheresearchongrowthan

3、dzeroesofsolutions，evenzeroesofitsderivatives，usingthemethodofcomplexanalysiSOnrthesispresentssomeresultsonentirefunctionssharingasmallfunctionwithitsderivativesandgrowthofsolutionsofnon—homogeneousdifferentialequationsT

4、hethesiSshowsthenewmethod，andourproofiSsimplerthanthatofthepreviousWegiveabriefsummaryasfollows1Letf(z)beanon—constantentirefunctionoffiniteorder，andlet口beanon—zerosmallfunctionoffIff與f‘‘’share口CM，then磐：cforcisan。nzcr。co

5、nstant；，一t22Letf(z1beanonconstantentirefunction，andlet口beanonzerosmallfunctionoffIffandf’，上(，)=anY扣’口。一1，‘”一1’aofshare口CM，wherea?！貽，a，(J=1，2，，H)areconstants，thenwehavetheexpressionoff；3Letf(z1beanon—constantentirefunctio

6、n，andlet盯beanon。zerosmallfunctionoffIffand，‘”’(z)，a，‘“’aof‘”’share口CM，whereaMl≠0，口Hareconstants，thenwehavetheexpressionoff；4Fordifferentialequationf‘e1ftQ(z)f=F(z1withentirefunctionsoffiniteorderasitscoefficientsIfQ(z)=h