几类差分方程周期边值问题的研究

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1、西北师范大学硕士学位论文几类差分方程周期边值问题研究姓名：马慧莉申请学位级别：硕士专业：@指导教师：马如云2008yoA&B~"(rppZ>D6~{BGF"8D*vrpUf6~{BGF"8D*E&)a,}UfvrpD}Uf6~{B"8D*℄b℄f*b℄[ra`x(k&83B℄rpo
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eq"rp℄vD**"va`t(Leray-SchauderrpTZ}Uf6~{BGF"8.D*∆2u(t−1)+λa(t)u(t)+g(t,u(t))=h(t),k(0.0.1)u(0)=u(T),u(1

2、)=u(T+1)b℄fuλkD*(0.0.1)"p℄Uf2D*℄`kÆ(08Z$a>0,gxÆl$X-VE/ZD*(0.0.1)b℄f:BeÆ;~{BGF"8D*℄~bfa`k(1rpUf6~{BGF"8D*2∆u(t−1)+λu(t)=0,(0.0.2)u(0)=u(T),u(1)=u(T+1)℄(08~-*(0$℄fATH?f,0℄hD*(0.0.2)(08℄℄hE)ZV(0$℄$(b℄V℄-p;~{BGF"8D*℄sÆ6~{BGF"8D*3^bBS[87]B'&x℄6~{

3、BGF"8D*(08℄:(08℄m℄E*V(0$℄$((:gBS[87]a℄2[`℄`(yu`k("℄VUfD*(0.0.2)℄(08aLeray-Schauderrp}Uf6~{BGF"8.D*∆2u(t−1)+λu(t)+g(t,u(t))=h(t),k(0.0.3)u(0)=u(T),u(1)=u(T+1)i

4、ySo+oA&Biip>b℄fuλkD*(0.0.2)℄`kÆ(08}UfX)Wxh-V℄):D*(0.0.3)p>b℄f93+℄p>b℄H?fZBe

5、Æ;~{BGF"8D*℄~bfa`G(yu`k("℄VUfD*(0.0.2)℄(08aRabinowitz[r~
&rp}Uf6~{BGF"8D*2∆u(t−1)+rf(u(t))=0,(0.0.4)u(0)=u(T),u(1)=u(T+1)$(b℄fuλkD*(0.0.2)℄`kÆ(08E/E3r℄W8y<y<:D*(0.0.4)=pÆ$(bRE$(b℄℄$(jx.~}3+℄b℄H?fZÆ0D*℄;~{BGF"8D*

6、~bfa"a~}#2bfa[11],[16],[48].`"(y^d

7、`k("℄VUfD*(0.0.2)℄(08aLeray-Schauder*~
hrp}Uf6~{BGF"8D*2∆u(t−1)+λu(t)+g(u(t))=h(t),(0.0.5)u(0)=u(T),u(1)=u(T+1)rÆp>b℄f}UfXUf%;℄-V℄h3λyÆλk℄,0W8y<,0y<:℄λ℄D*(0.0.5),0Æp>b℄f)R93+℄b℄H?f)xÆ6~{Bb(08(0$.b$(b~


8、ySo+oA&BiiiAbstractThisdissertationco

9、nsistsofsixchapters.Itsconcernfocusesonsometypepe-riodicboundaryvalueproblemsfordifferenceequations.Weinvestigatethespectralresultsofthelinearperiodicproblemandobtaintheexistenceresultsofsolutionsforsomenonlinearperiodicboundaryvalueproblemsofdifferenceequations.Thefirstcha

10、pterisprolegomenon,inwhichthestudyingbackground,theoret-icalframeofthisthesisareexhibited.Anditdisplaysthemainproblemwestudyandthemainresultsweobtain.Inthesecondchapter,applyingLeray-Schauderprinciple,westudythefollow-ingresonanceperiodicboundaryvalueproblemsofdifferencee

11、quations∆2u(t−1)+λa(t)u(t)+g(t,u(t))=h(t),k(0.0.1)u(0)=u(T),u(1)=u(T+1)withweightfunctiona(·).Theexi