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1、英文翻译下属学院理工学院专业信息与计算科学班级08信息与计算科学学号姓 名指导教师 2011年11月25日<文献翻译一：原文>SomePropertiesofSolutionsofPeriodicSecondOrderLinearDifferentialEquations1.IntroductionandmainresultsInthispaper,weshallassumethatthereaderisfamiliarwiththefundamentalresultsandthestardardnotationsoftheNevanlinna
2、'svaluedistributiontheoryofmeromorphicfunctions[12,14,16].Inaddition,wewillusethenotation，andtodenoterespectivelytheorderofgrowth,thelowerorderofgrowthandtheexponentofconvergenceofthezerosofameromorphicfunction，（[see8]），thee-typeorderoff(z),isdefinedtobeSimilarly,，thee-typeex
3、ponentofconvergenceofthezerosofmeromorphicfunction,isdefinedtobeWesaythathasregularorderofgrowthifameromorphicfunctionsatisfiesWeconsiderthesecondorderlineardifferentialequationWhereisaperiodicentirefunctionwithperiod.Thecomplexoscillationtheoryof(1.1)wasfirstinvestigatedbyBa
4、nkandLaine[6].Studiesconcerning(1.1)haveeencarriedonandvariousoscillationtheoremshavebeenobtained[2{11,13,17{19].Whenisrationalin，BankandLaine[6]provedthefollowingtheoremTheoremALetbeaperiodicentirefunctionwithperiodandrationalin.Ifhaspolesofoddorderatbothand,thenforeverysolu
5、tionof(1.1),Bank[5]generalizedthisresult:Theaboveconclusionstillholdsifwejustsupposethatbothandarepolesof,andatleastoneisofoddorder.Inaddition,thestrongerconclusion(1.2)holds.Whenistranscendentalin,Gao[10]provedthefollowingtheoremTheoremBLet,whereisatranscendentalentirefuncti
6、onwith,isanoddpositiveintegerand，Let.Thenanynon-triviasolutionof(1.1)musthave.Infact,thestrongerconclusion(1.2)holds.Anexamplewasgivenin[10]showingthatTheoremBdoesnotholdwhenisanypositiveinteger.Iftheorder,butisnotapositiveinteger,whatcanwesay?ChiangandGao[8]obtainedthefollow
7、ingtheoremsTheoremCLet,where,andareentirefunctionstranscendentalandnotequaltoapositiveintegerorinfinity,andarbitrary.(i)Suppose.(a)Iffisanon-trivialsolutionof(1.1)with;thenandarelinearlydependent.(b)Ifandareanytwolinearlyindependentsolutionsof(1.1),then.(i)Suppose(a)Iffisanon
8、-trivialsolutionof(1.1)with,andarelinearlydependent.Ifandareanytwoli
