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1、C^n中一类复高阶偏微分方程组的允许解Vo1.27(2007)NO.2数学杂:,tJ.ofMath.(PRC)ADMISSIBLESoLUTIoNSoFACLASSoFSYSTEMSoFHIGHER—ORDERPARTIALDIFFERENTIALEQUATIONSONCGAOLing—yun(Dept.ofMath.,JinanUniversity,Guangzhou510632,China)Abstract:Inthispaper,theproblemoftheexistenceofadmissiblemeromorphicsolutionsofflclassofs~emsofhighe
2、r-orderpartialdifferentialequationsinseveralcomplexvariablesisinvestigatedbyusingthevaluedistributiontheoryandtechniquesinseveralcomplexvariables.Somequalitiesofadmissiblemeromorphicsolutionsofflclassofsystemsofhigher-orderpartialdifferentialequationsundersomeconditionsareobtained.Someresultsofsyst
3、emsofdifferentialequationsaregeneralizedtoseveralcomplexvariables.Keywords:admissiblesolutions;severalcomplexvariables;systemsofpartialdifferentialequations2000MRSubjectClassification:32A22;35A20Documentcode:AArticleID:0255—7797(2007)02—0127—081Introduction2nLetMbeaconnectedcomplexmanifoldofdimensi
4、onandletA(M)一∑A(M)bem一0gradedringofCOOcomplexvalueddifferentialformsonM.EachsetA(M)canbesplitintofldirectsumA(M)一>:AM(M),whereA(M)istheformoftype(p,g).外口一ASflconsequence,thedifferentialoperatordonA(M)splitsintoa+a,wherea:Ap,(M)一A外(M),a:Ap'(M)一Ap'升(M).For一(1,…,)∈C",wedefine,foranyrER十,ll一(1ll.+…+
5、ll.).,r=ll.,C,l(r>一{∈C,l:ll—r),C,l(r)一{z∈C,l:ll<r).*Receiveddate:2005—02—28Accepteddate:2005一10-19Foundationitem:SupportedbyNationalNaturalScienceFoundationofChina(10471065);theNaturalScienceFoundationofGuangdongProvince(0401074).Biography:GaoLingyun(1963-).male,bornatQichun,Hubei,associatepr
6、ofessor,PostDoctor,majorinvaluedistributiontheoryandcomplexdifferentialequation.E—mial:tgaoly@jnu.edu.ca128JournalofMathematicsV01.27Let[r]:{∈:lI≤r},d----8+~,dc一÷(a—),wethenwrite儿cu()=ddlogff.,O"n()一dlogIzf.Acun--(),∈((0};"On()一ddlI,()一(),∈C".Thus()definesapositivemeasureon(r>withtotalmeasureon
7、eandisLebesguemeasureonnormalizedsuchthat(r)hasmeasure.Letfbeameromorphicfunctionon,i.e一厂canbewrittenasaquotientoftwoholomorphicfunctionswhicharerelativelyprime,letPbetheRiemannsphereP一cU{..}.Thusfcanberega
