差分方程的振动性的若干问题.pdf

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•P“±]Çƶ¡êƆOŽ‰ÆÆƉ;’A^êÆïÄ•••¼‡©•§nØ9ÙA^"˜cÊn›FSomeProblemsofOscillationofDifferenceEquationsCandidateZhenzhenZhangSupervisorProfessorYongZhouCollegeMathematicsandComputationalScienceProgramAppliedMathematicsSpe

2、cialityTheoryandApplicationsofFunctionalDierentialEquationsDegreeMasterofScienceUniversityXiangtanUniversityDateMay30th,2012‰ŒÆÆØ©M5(²¤JŠ¬.é©ïĉѕ‡z‡<Ú8N,þ®3©¥±²(•ªI².<¿£(²{ÆJd<«ú

3、.Šö¶µFϵcFÆØ©‡¦^ÇÖÆØ©Šö)Æk'3!¦^ÆØ©5½,Ó¿Æ3¿•I[k'Ü€½ÅxØ©E<‡Ú>f‡,#NØ©Ú/.<ljŒÆŒ±òÆØ©ܽܩSN?k'êâ¥?1u¢,Œ±æ^K

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5、^lÑTaylor'súªÚlÑKneser's½n,)û˜«©•§)Ä5;,,·‚

6、^k^‡ŠÑA‡íØ.313Ù,·‚ïĘa©•§k.)ÚÃ.)Ä57‡†¿©^‡.ÓžÿЕ§,¦ÙA^‰Œ•2•.'…c:¥á.©•§;Ä;AÄ;k.);Ã.);•ª).IAbstractInrecentyears,alotofpapersappearedaboutoscillationofdierenceequa-tions,lik

7、estorderdierenceequations,secondorderdierenceequations.but,comparedwiththehigherorderofdierenceequationsisnosoperfectinthetheory,manyareasarenotinvolved,weneedtodofurtherstudy.Inthispaper,wediscusstheoscillationofsolutionsofdierenceequationsandtheconditionsofoscill

8、ation.InChapter2,rstly,bytheuseofDiscreteKneser'stheoremandothertheorem,westudytheoscillationofsolutionsforcertainneutraldierenceequations;thenbytheuseoftheoriginalconditionwemakeseveralcorollary.InChapter3,byuseofDiscreteTaylor'sFormula,westudythenecessaryandsucient

9、conditionsfortheoscillationofboundedsolu-tionorunboundedsolutionofdierenceequations.Atthesametime,weexpandtheequation,soitcanmaketherangeofitsapplicationmorewidely.Keywords:neutraldierenceequation,oscillate,almostoscillate,unboundedsolution,boundedsolution,eventuallyp

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