C~n中复偏差分方程组的允许解英文.pdfVIP

应 用 数 学 MATHEMATICA APPLICATA 2015．28(2)：449-456 AdmissibleSolutionsofSystemsofComplex PartialDifferenceEquationsonC WANGYue(王钥)，ZHANGQingcai(张庆彩) (SchoolofInformation，RenminUniversityofChina，Beijing100872，China) Abstract：UsingtheNevanlinnatheoryofthevaluedistributionofmeromorphicfunctions，wein— vestigatetheexistenceofadmissiblemeromorphicsolutionsofaclassofsystemsofcomplexpartial differenceequationson ．Someexistingresultsareimprovedandgeneralized。andtwonew results areobtained．Examplesshow thatourresultsareprecise． Keywords：Valuedistribution；Admissiblesolution；Complexpartialdifferenceequation CLCNumber：0174．52 AMS(2000)SubjectClassification：30D35 Documentcode：A ArticleID：1001—9847(2015)02—0449—08 1．Introduction and M ainResults Inthispaper，weassumethatthereadersarefamiliarwith the standardnotation and basicresultsoftheNevanlinnatheoryofmeromorphicfunctionsrl一23 ． TherelatednotationsofthissectiontoTUE ． Let2一 (zl，… ， )∈ C”andr∈ R ．Introducingthedifferentialoperators， d ：一 8+ aandd ：一 (47ci) (a～ 3)， anddefining60()：一ddl‘ogI Iand ()：一d‘logI l^(u ()，where ∈C”＼{0) andj J：一flf+…+J I。． LetC”(r)一 (∈Ca：IzI—r)，C”(r)一 {z∈C ：I Ir)， Er]一 (z∈ ：I l≤ r)．Then口(z)definesapositivemeasureonCrwithtotalmeasureone．Inaddition，byde— fining ()：：=：a l l。andP (z)：一 ：()，forall ∈C ，itfollowsthatP()istheLebes— guemeasureon normalizedsuchthatC”(r)hasmeasurer2． Letw beameromorphicfunctiononC inthesensethat canbewrittenasaquotientof tworelativelyprimeholomorphicfunctions．Writew一 (训0，叫1)whereWo≠ 0，thuswcanbe regardedasameromorphicmapw ：C” P suchthatw- (。。)≠ C ． LetP betheRiemannsphere．Fora，b ∈ P ，thechordaldistancefrom atobisdenoted bylla，bll，lJa，o。ll一 (1+lal。) ，ll口，