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1、Æ“Ò10530ÆÒ200909031045©aÒO175—?©•§Ä5eZ¯KÆž<Ü•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{Æ Jd<«ú
3、.Šö¶µFϵcFÆØ©‡¦^ÇÖÆØ©Šö)Æk'3!¦^ÆØ©5½,Ó¿Æ3¿•I[k'Ü€½ÅxØ©E<‡Ú>f‡,#NØ©Ú/.<ljŒÆŒ±òÆةܽܩSN?k'êâ¥?1u¢,Œ±æ^K
4、ïÄ.3·Ø©ṗïÄ©•§)Ä59Ä^‡.312Ù,·‚Äk
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、estorderdierenceequations,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
10、ositivesolution.II8¹11ÙXØ........................................................(1)1.1ïĵ...................