简介：本文研究了Hilbert空间L^2（R^2）上由势函数V（x）（V≥0，连续）给出的一类Schrǒdinger算子H=-△＋V的谱。本文的主要结果：（1）H的谱σ（H）不会出现本性谱与离散谱交替出现的情况，其谱要么是离散的，要么从infσcos（H）开始全是本性谱；（2）lim‖x‖→∞V（x）=∞是σcos（H）=φ的充要条件。（3）借助于讨论H的Zhis-lin谱，在一定的条件下。lim‖x‖→∞V（x）=0是σcos（H）=[∞，0）的充要条件。我们还提出了几个没有解决的问题。

简介：Inthispaper,weinvestigatethesemiclassicallimitofthegeneralizednonlinearSchr?dingerequationforinitialdatawithSobolevregularity.Also,wewillanalyzethestructureofthefluiddynamicalsystemwithquantumeffectcorrespondingtothesemiclassicallimitofthegeneralizednonlinearSchr?dingerequation.

简介：Weprovetheexistenceandtheorbitalstabilityofstandingwavesforthenonau-tonomousSchrdingersystemiut+ua(x)u+(|u|2p+b(x)|u|p-1|v|p+1)u=0,x∈RN,ivt+va(x)v+|v|2p+b(x)|v|p-1|u|p+1v=0,x∈RNundersuitableconditionsonthecoefficientfunctionsaandb.Wefollowtheideaofanalyzingthecompactnessofminimizingsequenceoftheconstrainedminimizationproblems.

简介：LetL=-?+VbeaSchrdingeroperatoractingonL2(Rn),n≥1,whereV≡0isanonnegativelocallyintegrablefunctiononRn.Inthisarticle,wewillintropduceweightedHardyspacesHL(w)associatedwithLbymeansofthesquarefunctionandthenstudytheiratomicdecompositiontheory.WewillalsoshowthattheRiesztransform?L-1/2associatedwithLisboundedfromournewspaceHpL(w)totheclassicalweightedHardyspaceHp(w)whenn/(n+1)

简介：Inthispaper,severalnewconstant-amplitudeandvariable-amplitudewavesolutions(namely,travelingwavesolutions)ofageneralizednonlinearSchrdingerequationareinvestigatedbyusingtheextendedhomogeneousbalancemethod,wherethebalancemethodisappliedtosolvetheRiccatiequationandthereducednonlinearordinarydifferentialequation,respectively.Inaddition,stabilityanalysisofthosesolutionsarealsoconductedbyregularphaseplanetechnique.

简介：ThefollowingcoupledSchrdingersystemwithasmallperturbationuxx+u-u3+βuv2+f(,u,ux,v,vx)=0inR,vxx-v+v3+βu2v+g(,u,ux,v,vx)=0inRisconsidered,whereβandaresmallparameters.ThewholesystemhasaperiodicsolutionwiththeaidofaFourierseriesexpansiontechnique,anditsdominantsystemhasaheteroclinicsolution.Thenadjustingsomeappropriateconstantsandapplyingthefixedpointtheoremandtheperturbationmethodyieldthatthisheteroclinicsolutiondeformstoaheteroclinicsolutionexponentiallyapproachingtheobtainedperiodicsolution(calledthegeneralizedheteroclinicsolutionthereafter).

简介：TheprimarygoalofthispaperistopresentacomprehensivestudyofthenonlinearSchrdingerequationswithcombinednonlinearitiesofthepower-typeandHartreetype.Undercertainstructuralconditions,theauthorsareabletoprovideacompletepictureofhowthenonlinearSchrdingerequationswithcombinednonlinearitiesinteractinthegivenenergyspace.ThemethodusedinthepaperisbasedupontheMorawetzestimatesandperturbationprinciples.

简介：Byusingthemethodofdynamicalsystem,theexacttravellingwavesolutionsofthecouplednonlinearSchrdinger-KdVequationsarestudied.Basedonthismethod,allphaseportraitsofthesystemintheparametricspacearegiven.Allpossibleboundedtravellingwavesolutionssuchassolitarywavesolutionsandperiodictravellingwavesolutionsareobtained.WiththeaidofMaplesoftware,thenumericalsimulationsareconductedforsolitarywavesolutionsandperiodictravellingwavesolutionstothecouplednonlinearSchrdinger-KdVequations.Theresultsshowthatthepresentedfindingsimprovetherelatedpreviousconclusions.

简介：本文运用一种变量代换将非线性Sdhrodinger方程转变为半线性椭圆型方程,再利用山路引理,Lion集中紧引理,Soblev嵌入不等式证明一类Schrodinger方程孤子解的存在性.

简介：Thispaperdisccussestheinversescatteringproblemforone-dimensionalSchrodingeroperatorsrelatedtothegeneralStarkeffect.WeprovideaganeralframeworkwhichcanbeappliedbothtotheStark-effectoperatorandtheordinarySchrodingeroperator.

简介：LetL=L0+VbethehigherorderSchrdigertypeoperatorwhereL0isahomogeneousellipticoperatoroforder2mindivergenceformwithboundedcoefficientsandVisarealmeasurablefunctionasmultiplicationoperator(e.g.,including(-?)m+V(m∈N)asspecialexamples).Inthispaper,assumethatVsatisfiesastronglysubcriticalformconditionassociatedwithL0,theauthorsattempttoestablishatheoryofHardyspaceHpL(Rn)(0

简介：LetG？R2bearegularanisotropicfractal.WediscusstheproblemofthenegativespectrumfortheSchr¨odingeroperatorsassociatedwiththeformalexpressionHb=id？D＋btrGb,b∈R,actingintheanisotropicSobolevspaceW1,a2（R2）,whereDistheDirichletLaplanianinR2andtrGbisafractalpotential（distribution）supportedbyG.

简介：以广义逆为工具运用算子演算给出加权移位算子是次正常算子的条件，所用方法不同于Ｓｔａｍｐｆｌｉ的工作，但结果一致．作为应用给出了两个例子．

简介：设初等算子E(X)=∑AiXBi,定义E*(X)=∑Ai*XBi*.我们证明了EE*=E*E当且仅当{Ai}和{Bi}都是交换的正规算子族,从而回答了由D.Keckic提出的关于初等算子正规性的开问题.我们还给出了E=E*的充分必要条件.

简介：针对现有灰色预测模型主要以一阶累加生成序列作为建模序列，再累减还原为原始序列预测值，本文通过Gamma函数将累加生成算子和累减生成算子拓展到正实数领域，给出分数阶累加生成算子和分数阶累减生成算子的解析表达式，一阶和整数阶均是其特例，证明了两算子之间的互逆性．为建立分数阶灰色预测模型和拓宽灰色预测模型的应用范围提供理论基础．

简介：设X是自反Banach空间且X和X^*均为局部一致凸空间，D是X的开、有界、凸子集，T：D→X^*是伪单调算子（pseudo-monotone),C:D→X^*是紧算子或全连续算子。利用（S+）型算子的度理论，我们建立了T+C值域性质的几个结果，这些结果对研究各类方程问题有所应用。

简介：设M^2n+1(K)是2n+1维常ψ—截面曲率K的紧致Sasaki流形，本文证明了与M^2n+1(K)等谱的上同调Einstein的紧致Sasaki流形必有常ψ-截面曲率K．

简介：设ｉＡｊ（１≤ｊ≤）是有界Ｃ０群的可交换生成元，Ｐ（Ａ）＝∑｜μ｜≤２ａμＡμ（Ａμ＝Ａ１μ…Ａｎμｎ）如果Ｐ是弱椭圆的且其实部是上有界的，则我们证明Ｐ（Ａ）生成一个Ｃ０半群．

简介：设g1．g2为正规函数．对所有的0〈p．q〈∞，我们得到了Bergma型空间的加权Cesaro算子Tψ：Ag1^p→Ag2^q为有界算子和紧算子的充要条件．

简介：Ю.И.Волков在[1]中构造了一系列一元及多元线性算子，其中包括二元Baskakov算子，本文讨论该算子在C空间的逼近性质。