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

简介：在这篇论文，我们为解决与错误建议并且分析一个三步的反复的计划非线性强烈没有Lipshitzcondition的accretive操作员方程Tx=f。在这篇论文介绍的结果在更一般的背景改进并且延长当前的结果。

简介：Considerasystemofnonlinearwaveequations(e)2t-c2i△xui=Fi(u,(e)u,(e)x(e)u)in(0,∞)×(R)3fori=1,┈,m,whereFi(i=1,┈,m)aresmoothfunctionsofdegree2neartheoriginoftheirarguments,andu=(u1,┈,um),while(e)uand(e)x(e)urepresentthefirstand(secondderivativesofu,respectively.Inthispaper,theauthorpresentsanewclassofnonlinearityforwhichtheglobalexistenceofsmallsolutionsisensured.Forexample,globalexistenceofsmallsolutionsfor((e)2t-c21Δx)u1=u2((e)tu2)+arbitrarycubicterms,((e)2t-c22Δx)u2=u1((e)tu2)+((e)tu1)u2+arbitrarycubictermswillbeestablished,providedthatc21≠c22.

简介：这份报纸的目的是为任何特定的热比率在3证明稳定的可压缩的isentropicMHD方程的一个空间地周期的弱答案的存在>1。证明为导致弱集中的密度，和方法的某更高的integrability的近似系统基于压力和动能的加权的估计。根据作者知识，是第一结果在三种尺寸对待稳定的可压缩的MHD方程的弱答案的存在与>1。

简介：在这篇文章，我们认为非线性的秒顺序的二个积极答案的存在是三点的单个边界价值问题：?u(t)=f(t，u(t))为，使=0和u()=u(1)遭到到u(0)的所有t(0,1)0,1)，[0,1)，并且是一个积极参数。非线性的术语f(t，u)是nonnegative，并且可能在t=0，t=1，和u=0单个。由固定的点索引理论和近似方法，我们证实那在那里存在*(0，+]以便上述问题为任何东西有至少二个积极答案(0，*)在非线性的条款f上的某些条件下面。

简介：在这份报纸，我们建议一个维的切开方法为三维(3D)旋转海军司烧方程。假设领域是二表面围住的一条隧道

简介：ThediscreteSobolev’sinequalitiesinL_pnormareprovedforthree-dimensionalsphericalandcylindricalcoordinates,byusingdiscreteHolderinequality.propertyofthetrianglefunctionsandcomplicateddeduction.

简介：Thepurposeofthispaperistoinvestigatesomesufficientandnecessaryconditionsforthree-stepIshikawaiterativesequenceswitherrortermsforuniformlyquasi-Lipschitzianmappingstoconvergetofixedpoints.OurresultsextendandimprovetherecentonesannouncedbyLiu[3,4],XuandNoor[5],andmanyothers.

简介：Inthispaperwediscusstheexistenceofatleastthreesolutionsforaclassofgradientmixedboundaryvaluesystems.TheapproachisfullybasedonarecentthreecriticalpointstheoremofB.Ricceri[Athreecriticalpointstheoremrevisited,NonlinearAnal.,70:9(2009),3084-3089].

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简介：Weusetheincrementalunknownsmethodinconjunctionwiththeiterativemethodstoapproximatethesolutionofthenonsymmetricandpositive-definitelinearsystemsgeneratedfromamultileveldiscretizationofthree-dimensionalconvection-diffusionequations.Theconditionnumbersofincrementalunknownsmatricesassociatedwiththeconvection-diffusionequationsandthenumberofiterationsneededtoattainanacceptableaccuracyareestimated.Numericalresultsarepresentedwithtwo-levelapproximations,whichdemonstratethattheincrementalunknownsmethodwhencombinedwithsomeiter-ativemethodsisveryeffcient.

简介：InthepresentpaperweintroducearandomiterationschemeforthreerandomoperatorsdefinedonaclosedandconvexsubsetofauniformlyconvexBanachspaceandproveitsconvergencetoacommonfixedpointofthreerandomoperators.Theresultisalsoanextensionofaknowntheoreminthecorrespondingnon-randomcase.

简介：Thesoftwareforoil-gastransportandaccumulationistodescribethehistoryofoil-gastransportandaccumulationinbasinevolution.Itisofgreatvalueinrationalevaluationofprospectingandexploitingoil-gasresources.Themathematicalmodelcanbediscribedasacoupledsystemofnonlinearpartialdifferentialequationswithmovingboundaryvalueproblem.Foragenericcaseofthethree-demensionalboundedregion,bithisthesis,theeffectsofgravitation、buoyancyandcapillarypressureareconsidered,weputforwardakindofcharacteristicfinitedifferenceschemesandmakeusethickandthingridstoformacompleteset,andofcalculusofvaviations,thechangeofvariable,thetheoryofpriorestimatesandtechniques,Optimalorderestimatesinl~2normarederivedfortheerrorinapproximateassumption,Thuswehavecompletelysolvedthewell-knowntheoreticalproblemproposedbyJ.Douglas,Jr.

简介：Thispaperpresentsalternatingdirectionfinitevolumeelementmethodsforthree-dimensionalparabolicpartialdifferentialequationsandgivesfourcomputationalschemes,oneisanalogoustoDouglasfinitedifferenceschemewithsecond-ordersplittingerror,theothertwoschemeshavethird-ordersplittingerror,andthelastoneisanextendedLODscheme.TheL2normandH1semi-normerrorestimatesareobtainedforthefirstschemeandsecondone,respectively.Finally,twonumericalexamplesareprovidedtoillustratetheefficiencyandaccuracyofthemethods.

简介：ＦＯＵＲＩＥＲ－ＣＨＥＢＹＳＨＥＶＳＰＥＣＴＲＡＬＭＥＴＨＯＤＦＯＲＳＯＬＶＩＮＧＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＶＯＲＴＩＣＩＴＹＥＱＵＡＴＩＯＮＧＵＯＢＥＮＹＵ（郭本瑜）；ＬＩＪＩＡＮ（李健）；ＭＡＨＥＰＩＮＧ（马和平）（Ｄｅｐａｒｔｍｅｎｔｏ...

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简介：Inthispaper,bifurcationofsmallamplitudelimitcyclesfromthedegenerateequilibriumofathree-dimensionalsystemisinvestigated.Firstly,themethodtocalculatethefocalvaluesatnilpotentcriticalpointoncentermanifoldisdiscussed.Thenanexampleisstudied,bycomputingthequasi-Lyapunovconstants,theexistenceofatleast4limitcyclesonthecentermanifoldisproved.Intermsofdegeneratesingularityinhigh-dimensionalsystems,ourworkisnew.

简介：Inthispaper,Chebyshevpseudospectral-finiteelementschemesareproposedforsolvingthreedimensionalvorticityequation.SomeapproximationresultsinnonisotropicSobolevspacesaregiven.Thegeneralizedstabilityandtheconvergenceareprovedstrictly.Thenumericalresultsshowtheadvantagesofthismethod.Thetechniqueinthispaperisalsoapplicabletootherthree-dimensionalnonlinearproblemsinfluiddynamics.