简介：Thebundleofthe2-formson6-manifolddecomposesintothreesubbundlessuchthatΛ2（R6）=Λ21⊕Λ26⊕Λ28withdimensions1,6and8,respectively.Theselfandantiselfdualitysolutionsofthe2-forms,calledΦ-duality,arehandledandthesesolutionsshowthattheantiselfdualgaugefieldsliveonthesubbundlesΛ21andΛ26whiletheselfonesequationsonΛ28.AlsothesolutiononΛ21presentsaflatconnection.Inaddition,thecurvaturesoftheconnectionsonΛ26andΛ28haveTr[F3]=0,andsothetopologicalinvariantsdeterminedbytheChernclasses,i.e.topologicalcharge,consistonlyonthesecondChernclass.Intheresultofthiscase,theantiselfandselfΦ-dualgaugeinvariantLagrangiansofdefinedonbothsubbundlesareboundedbythesametopologicalcharge.Also,onegivesaquantizationcasetoberelatingtotheinstantonnumber.

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简介：Inthispaper,byusingtheGuo-Krasnoselskii'sfixed-pointtheorem,weestablishtheexistenceandmultiplicityofpositivesolutionsforafourth-ordernonlineareigenvalueproblem.Thecorrespondingexamplesarealsoincludedtodemonstratetheresultsweobtained.

简介：Inthispapertheexistenceresultsofpositiveω-periodicsolutionsareobtainedforsecondorderordinarydifferentialequation-u″(t)=f(t,u(t))(t∈R),andalsoforfirstorderordinarydifferentialequationu′(t)=f(t,u(t))(t∈R),wheref:R×R+→Risacontinuousfunctionwhichisω-periodicint.Thediscussionisbasedonthefixedpointindextheoryincones.

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简介：这份报纸描述分析、数字的方法与对称的橡皮和惯性非线性分析一个振荡器的稳定的州的周期的反应。homotopy不安方法(HPM)和调用max-min途径的一个古老的中国方法的新实现被介绍获得一个近似答案。主要担心是在由检验他们的能力建立在系统参数的某个范围以内预言系统反应估计这些近似方法的精确性一实际(数字)答案。因此，分析结果与数字结果相比说明建议方法的有效性和便利。关键词非线性的摆动-homotopy不安方法(HPM)-max-min途径(MMA)-Rung-Kutta方法(R千米；公里)-大振幅免费颤动

简介：我们与nonmonotone不安为微分包括处理抗周期性病药问题。在我们的学习的主要工具是有抗周期性病药条件和最大的单调mappings的pseudomonotone不安的理论的衍生物操作员的最大的单调性质。我们然后与nonmonotone断绝把我们的结果用于进化hemivariational不平等和寓言的方程，它概括并且延长以前已知的定理。

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简介：Theseriescomposedbybeammodefunctionisusedtoapproximatethedisplacementfunctionofconstraineddampingoflaminatedcantileverplates,andthetransversedeformationoftheplateonwhichaconcentratedforceisactediscalculatedusingtheprincipleofvirtualwork.BysolvingLagrange'sequation,thefrequenciesandmodellossfactorsoffreevibrationoftheplateareobtained,thenthetransientresponseofconstraineddampingoflaminatedcantileverplateisobtained,whentheconcentratedforceiswithdrawnsuddenly.Thetheoreticalcalculationsarecomparedwiththeexperimentaldata,theresultsshow:boththefrequenciesandtheresponsetimeoftheoreticalcalculationanditsvariationallawwiththeparametersofthedampinglayerareidenticalwithexperimentalresults.Also,theresponsetimeofsteelcantileverplate,unconstraineddampingcantileverplateandconstraineddampingcantileverplatearebroughtintocomparison,whichshowsthattheconstraineddampingstructurecaneffectivelysuppressthevibration.

简介：Thispaperisasequeltoapreviouspaper(Yang,Y.andZhang,J.H.Existenceofsolutionsforsomefourth-orderboundaryvalueproblemswithparameters.NonlinearAnal.69(2),1364–1375(2008))inwhichthenontrivialsolutionstothefourthorderboundaryvalueproblemswerestudied.Inthecurrentworkwiththesameconditionsnearinfinitybutdifferentnearzero,thepositive,negative,andsign-changingsolutionsareobtainedbythecriticalpointtheory,retractingproperty,andinvariantsets.

简介：我们学习二维的non-self-similar的一个家庭的单个结构quasilinear的全球解决方案和他们的相互作用夸张能量守恒定律。当起始的断绝在仅仅上发生时，为盒子，二拆散统一圆和起始的数据是二个不同经常的状态，全球答案被构造，一些新现象被发现。在分析，我们首先为0t构造答案T，在二个冲击波之间的另一个冲击波发生。最后，我们给答案的大时间行为什么时候t。这种技术不包含维的减小或并列转变。

简介：ThepurposeofthispaperistouseaveryrecentthreecriticalpointstheoremduetoBonannoandMaranotoestablishtheexistenceofatleastthreesolutionsforthequasilinearsecondorderdifferentialequationonacompactinterval[a,b]?R{-u’’=(λf(x,u)+g(u))h(u’),in(a,b),u(a)=u(b)=0underppropriatehypotheses.Weexhibittheexistenceofatleastthree(weak)solutionsand,andtheresultsareillustratedbyexamples.

简介：§1.IntroductionInthispaperweconsidertheparabolicsystem（?）t/（?）ui-div(|▽u|p-2▽ui)=0（1≤i≤m）,withp>1,whereui=ui（x,t）,▽=gradxandxvariesinanopendomainΩ（?）RN.Thesystemisdegenerateifp>2orsingularif1

简介：Lin-Reissner-Tsien方程在接近音速的近似下面描述不稳定的接近音速的流动。在现在的纸，方程经由类似转变被归结为一个平常的微分方程。产生方程是然后解决的经分解并且完全在一些情况中弄平。数字模拟被为没有准确答案的在盒子提供。旅行波浪答案也被获得。

简介：Inthispaper,weconsiderexistenceanduniquenessofpositivesolutionstothreecouplednonlinearSchrdingerequationswhichappearinnonlinearoptics.Weusethebehaviorsofminimizingsequencesforaboundtoobtaintheexistenceofpositivesolutionsforthreecoupledsystem.Toprovetheuniquenessofpositivesolutions,weusetheradialsymmetryofpositivesolutionstotransformthesystemintoanordinarydifferentialsystem,andthenintegratethesystem.Inparticular,forN=1,weprovetheuniquenessofpositivesolutionswhen0≤β=μ1=μ2=μ3orβ>max{μ1,μ2,μ3}.

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简介：WeinvestigatethenonlinearSchrdingerequationiut+△u+|u|p-1u=0with1+4/N||Q||（1-sc）/sc|▽Q||2,theneitheru（t）blowsupinfiniteforwardtimeoru（t）existsgloballyforpositivetimeandthereexistsatimesequencetn→+∞suchthat||▽u（tn）||2→+∞.HereQisthegroundstatesolutionof—（1—sc）Q+△Q+|Q|p-1Q=0.Asimilarresultholdsfornegativetime.Thisextendtheresultofthe3DcubicSchr（o|¨）dingerequationobtainedbyHolmertothegeneralmass-supercriticalandenergy-subcriticalcase.

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简介：Thispaperaimstodevelopapowerpenaltymethodforalinearparabolicvariationalinequality(Ⅵ)intwospatialdimensionsgoverningthetwo-assetAmericanoptionvaluation.Thismethodyieldsatwo-dimensionalnonlinearparabolicPDEcontainingapowerpenaltytermwithpenaltyconstantλ>1andapowerparameterk>0.WeshowthatthenonlinearPDEisuniquelysolvableandthesolutionofthePDEconvergestothatoftheⅥattherateoforder(?)(λ~(-k/2)).AfittedfinitevolumemethodisdesignedtosolvethenonlinearPDE,andsomenumericalexperimentsareperformedtoillustratetheusefulnessofthismethod.

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