29524.復域差分及差分方程亞純解的值分布

1、(用作檔案留存的學位論文才需填寫此合格證明)II華南師范大學博士學位論文AbstractIntherecentyears，differenceanddifferenceequationsinthecomplexplanebecomeanewheatsubjectinthecomplexanalysisManyauthorshaveobtainedfruitfulresultsInthisthesis：wemainlyuseNevanli

2、nna’Svaluedistributiontheorytoinvestigatethevaluedistributionofcomplexdifferences，meromorphicsolutionsofdifferencePainlev6IIIequations，andsomedifferencepolynomialsThereatefourchaptersinthisthesisInChapterl，weintroducebas

3、icconceptsandnotationsWealsointroducesomefun—damentalresultsofNevanlinna’SvaluedistributiontheoryandtheirdifferenceanaloguesandthebackgroundofdifferencePainlev6equationsInChapter2，weinvestigatethecharacteristicfunctionan

4、dvaluedistributionofthen：sforwarddifference△”，(z)，wheref(z)isafiniteordermeromorphicfunctionwithtwoBorelexceptionalvaluesFirstlyweobtainthepreciserelationshipsofcharacteristicrunetionsbetweenA“f(z)and，(z)，unlessfiz)andit

5、sshiftCsatisfysomespecialconditions；SecondlywestudyvaluedistributionofA”f，undersomeconditionsweobtain0or0ando。aretheNevanlinnaexceptionalvaluesof△“f(z1InChapter3，weinvestigatepropertiesofmeromorphicsolutionsofdifferenceP

6、ainlev6IIIequations，suchasthevaluedistributionofmeromorphicsolutiomeromorphicsolutionsandtheirshifts，theexponentsofconvergenceofdifferenceanddivideddifferenceofmeromorphicsolutionsns，fixedpointsofofzerosandpolesInChapter

7、4：westudythevaluedistributionofdifferencepolynomialsoftheformQ(z，f)=，(三)“P(z，f)whereP(z，f)isadifferencepolynomial，and凡之d(P)1or禮≥d(P)2whered(P)denotesthedegreeofp(z，f)withrespecttofKeywords：Nevanlinnatheory；valuedistribut