信息与计算科学专业可控的无穷时滞中立型泛函微分方程大学毕业论文外文文献翻译及原文

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1、文献文献文献文献专业：信息与计算科学班级：姓名：学号：院指导教师:翻译日期:2017.02.14毕业设计（论文）外文文献翻译、资料中文题目：可控的无穷时滞中立型泛函微分方程、资料英文题目：、资料来源：、资料发表（出版）日期：（部）：英文翻译〈文献翻译一：原文〉SomePropertiesofSolutionsofPeriodicSecondOrderLinearDifferentialEquations1.IntroductionandmainresultsInthispaper，wcshallassumethatthereaderisfamiliarwiththe

2、fundamentalresultsandthestardardnotationsoftheNevanlinna.svaluedistributiontheoryofmcromorphicfunctions[12,14,16].Inaddition,wewillusethenotation€T(/)，"(/)andA(f)todenoterespectivelytheorderofgrowth，thelowerorderofgrowthandtheexponentofconvergenceofthezerosofamcromorphicfunctionf，Gc(/)

3、([see8]),thee-typeorderoff(z)，isdefinedtobeSimilarly,Ae(/),thee-typeexponentofconvergenceofthezerosofmcromorphicfunctionf，isdefinedtobe人（/）=log+7V(r，l//)Wesaythatf(z)hasregularorderofgrowthifameromorphicfunctionf(z)satisfies(7(/)=limlogr(r，/)logrWeconsiderthesecondorderlineardifferenti

4、alequation广+0WhereA(z)=)isaperiodicentirefunctionwithperiod0)=2m/(X.Thecomplexoscillationtheoryof(1.1)wasfirstinvestigatedbyBankandLaine[6].Studiesconcerning(1.1)haveccncarriedonandvariousoscillationtheoremshavebeenobtained[2{11，13，17{19].WhenA(z)isrationaline°^,BankandLaine[6]provedth

5、efollowingtheoremTheoremALetA(z)=6(erz:)beaperiodicentirefunctionwithperiodO)=2m/aandrationaline°^.Ifhaspolesofoddorderatboth=ooand(=0，thenforeverysolutionf(2)(矣0)of(1.1),A(/)=+°°Bank[5]generalizedthisresult:Theaboveconclusionstillholdsifwcjustsupposethatboth^=°°and=0arepolesof5(()，and

6、atleastoneisofoddorder.Inaddition,thestrongerconclusionlog+(1.2)holds.WhenA(z)istranscendental[ne02,Gao[10]provedthefollowingtheoremTheoremBLetS(O=g(l/O+AOereg(r)isatranscendentalentirefunctionwith(7(公)<1，/?isanoddpositiveintegerand0,LetA(z)=).Thenanynon-triviasolutionfof(1.1)musthaveA

7、(/)=.Infact,thestrongerconclusion(1.2)holds.Anexamplewasgivenin[10]showingthatTheoremBdocsnotholdwhen(7(g)isanypositiveinteger.Iftheorder<7(g)>1，butisnotapositiveinteger,whatcanwesay?ChiangandGao[8]obtainedthefollowingtheoremsTheoremCLetA(z)=B(^o::),whereS(^)=g,(l/^)+g2(^),g}andg2arc