SomePropertiesofSolutionsofPeriodicSecondOrderLinearDifferentialEquationsIntroductionandmainresultsInthispaper,weshallassumethatthereaderisfamiliarwiththefundamentalresultsandthestardardnotationsoftheNevanlinna'svaluedistributiontheoryofmeromorphicfunctions[12,14,16].Inaddition,wewillusethenotation,andtodenoterespectivelytheorderofgrowth,thelowerorderofgrowthandtheexponentofconvergenceofthezerosofameromorphicfunction,([see8]),thee-typeorderoff(z),isdefinedtobeSimilarly,,thee-typeexponentofconvergenceofthezerosofmeromorphicfunction,()wasfirstinvestigatedbyBankandLaine[6].Studiesconcerning()haveeencarriedonandvariousoscillationtheoremshavebeenobtained[2{11,13,17{19].Whenisrationalin,BankandLaine[6],thenforeverysolutionof(),Bank[5]generalizedthisresult:Theaboveconclusionstillholdsifwejustsupposethatbothandarepolesof,,thestrongerconclusion(),Gao[10]provedthefollowingtheoremTheoremBLet,whereisatranscendentalentirefunctionwith,isanoddpositiveintegerand,-triviasolutionof(),thestrongerconclusion()[10],butisnotapositiveinteger,whatcanwesay?ChiangandGao[8]obtainedthefollowingtheoremsTheorem1Let,where,andareentirefunctionswithtranscendentalandnotequaltoapositiveintegerorinfinity,(),thenOrWeremarkthattheconclusionofTheorem1remainsvalidifweassumeisnotequaltoapositiveintegerorinfinity,andarbitraryandstillassume,Inthecasewhenistranscendentalwithitslowerorder
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