復(fù)高階代數(shù)微分方程(組)的亞純解.pdf

1、山東大學(xué)博士后士學(xué)位論文復(fù)高階代數(shù)微分方程（組）的亞純解姓名：高凌云申請學(xué)位級別：博士后士專業(yè)：數(shù)學(xué)指導(dǎo)教師：儀洪勛2000.6.1AbstractUsingNevanlinnatheoryofthevaluedistributionofmeromorphicfunctions，wefurtherinvestigatesomeproblemsofmeromorphicsolutionsof(systemsof)differentiale

2、quationsandobtainsomeresultsThispapercontainsninechaptersChapterlisconcernedwiththebasicdefinitionsandnotationsInchapter2weinvestigatetheMalmquisttypeTheoremofadmissiblealgebroidsolutionofdifferentialequationsandobtainso

3、meresultsWehaveexamplestodemon—stratethatourresultsarebetterthanthepreviousonesInchapter3westudythegrowthofgeneralizedalgebraicdifferentialequation，andobtainsomeresultsInchapter4withaidofSteinmetz’Smethod，weinvestigateat

4、ypeofsystemofcomplexalgebraicdifferentialequationswhichstudysoldemandobtainaanalogousresultwithgeneralizedalgebraicdifferentialequationInchapter5wediscusstheproblemtheexistenceofadmissiblemeromorphicsolutionofseveraltype

5、sofsystemsofalgebraicdifferentialequations，ontheonehand，westudyconditionssuchthatsystemsofalgebraicdifferentialequationsexistadmissiblemeromorphicsolutions；ontheotherhand，weinvestigatetheformofthecorrespond—ingsystemsofa

6、lgebraicdifferentialequationsafterimposingsomerequirementsofthequalityofthesolution，andobtainfurtherresultswhichexactandimpovethepreviousonesMoreover，wealsodiscusstheproblemtheexistenceofnonadmissiblemeromorphicsolutiono

7、fatypeofasystemofalgebraicdifferentialequationsandobtainaresultInchapter6wegivethedefinitionofmcomponentsadmissiblesolutionofasystemofseveralclassesofsystemsofalgebraicdifferentialequationsanddiscusstheexistenceproblemao

8、fitsseveralclassesforthefirsttimeandobtainseveraltheo—remsExamplesshowourupperboundcanbereachedInchapter7wewillconsidertheproblemofthevaluedistributionoftwopolynomialsinanadmissiblesolutionandthedistributionofadmissibles

9、olutionsTheoremsaredevotedtotheinvestigationofthemfunctionandNfunction，respectivelyInchapter8wemainlydisscusstheformsofsolutionsoftwotypesofsystemsofspecificalgebraicdifferentialequationsItisbeneficialtostudyofqualityofs