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1.
In this paper, by means of Olsen type inequalities related to the fractional integral operator, the authors establish the interior estimates in Morrey spaces for Schrdinger type elliptic equations with potentials satisfying a reverse Hlder condition.  相似文献   

2.
《数学学报》2011,(5):885-888
<正>Schrdinger Soliton from Lorentzian Manifolds Chong SONG You De WANG Abstract In this paper,we introduce a new notion named as Schrdinger soliton.The socalled Schrdinger solitons are a class of solitary wave solutions to the Schrdinger flow equation from a Riemannian manifold or a Lorentzian manifold M into a Khler manifold N.If the target manifold N admits a Killing potential,then the Schrdinger soliton reduces to a harmonic  相似文献   

3.
Let ∠= -△H~n+ V be the Schrdinger operator on the Heisenberg groups H~n,where V is a nonnegative function satisfying the reverse Hlder inequality. In this article, the author obtains the BMO_∠ and BLO_∠ estimates of the fractional integrals associated to ∠.  相似文献   

4.
Addressed here is the occurrence of point singularities which owe to the focusing of short or long waves, a phenomenon labeled dispersive blow-up. The context of this investigation is linear and nonlinear, strongly dispersive equations or systems of equations. The present essay deals with linear and nonlinear Schrdinger equations, a class of fractional order Schrdinger equations and the linearized water wave equations, with and without surface tension. Commentary about how the results may bear upon the formation of rogue waves in fluid and optical environments is also included.  相似文献   

5.
In this paper, we investigate the semiclassical limit of the generalized nonlinear Schrdinger equation for initial data with Sobolev regularity. Also, we will analyze the structure of the fluid dynamical system with quantum effect corresponding to the semiclassical limit of the generalized nonlinear Schrdinger equation.  相似文献   

6.
The authors prove Carleman estimates for the Schrdinger equation in Sobolev spaces of negative orders, and use these estimates to prove the uniqueness in the inverse problem of determining Lp-potentials. An L2-level observability inequality and unique continuation results for the Schrdinger equation are also obtained.  相似文献   

7.
In this article, the authors characterize pointwise multipliers for localized MorreyCampanato spaces, associated with some admissible functions on RD-spaces, which include localized BMO spaces as a special case. The results obtained are applied to Schrdinger operators and some Laguerre operators.  相似文献   

8.
In this paper,we follow Dappa’s work to establish the Marcinkiewicz criterion for the spectral multipliers related to the Schrdinger operator with a constant magnetic field.We prove that if m and m′are locally absolutely continuous on(0,∞)and ‖m‖∞+sup j∈Z2j 2i+1 r|m′′(r)|dr∞,then the multiplier defined by m(t)is bounded on Lpfor 2n/(n+3)p2n/(n-3)with n 3.Our approach is based on the estimates for the generalized Littlewood-Paley functions of the spectral representation of the Schrdinger operator with a constant magnetic field.  相似文献   

9.
Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator Tbf = bTf-T(bf) on Lp , p∈(1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b∈BMOθ(X)BMO(X). Moreover, they prove that Tb is bounded from the Hardy space H1ρ(X) into the weak Lebesgue space L1weak(X). This can be used to deal with the Schrdinger operators and Schrdinger type operators on the Euclidean space Rn and the sub-Laplace Schrdinger operators on the stratified Lie group G.  相似文献   

10.
The authors study the compressible limit of the nonlinear Schrdinger equation with different-degree small parameter nonlinearities in small time for initial data with Sobolev regularity before the formation of singularities in the limit system.On the one hand,the existence and uniqueness of the classical solution are proved for the dispersive perturbation of the quasi-linear symmetric system corresponding to the initial value problem of the above nonlinear Schrdinger equation.On the other hand,in the limi...  相似文献   

11.
带乘性噪声的空间分数阶随机非线性Schrödinger方程是一类重要的方程,可应用于描述开放非局部量子系统的演化过程.该方程为一个无穷维分数阶随机Hamilton系统,且具有广义多辛结构和质量守恒的性质.针对该方程的广义多辛形式,在空间上采用拟谱方法离散分数阶微分算子,在时间上则采用隐式中点格式,构造出一类保持全局质量的广义多辛格式.对行波解和平面波解等进行数值模拟,结果验证了所构造格式的有效性和保结构性质,时间均方收敛阶约在0.5到1之间.  相似文献   

12.
In this article,we show the existence of infinitely many solutions for the fractional pLaplacian equations of Schr?dinger-Kirchhoff type equation ■ ,where(-△)_p~s is the fractional p-Laplacian operator,[u]_(s,p) is the Gagliardo p-seminorm,0 s 1 q p N/s,α∈(0,N),M and V are continuous and positive functions,and k(x) is a non-negative function in an appropriate Lebesgue space.Combining the concentration-compactness principle in fractional Sobolev space and Kajikiya's new version of the symmetric mountain pass lemma,we obtain the existence of infinitely many solutions which tend to zero for suitable positive parameters λ and β.  相似文献   

13.
夏滨 《数学学报》2017,60(5):799-814
在关于非相对论分子物理中磁性粒子捕获电子的研究中,带逆平方势的非线性Schr?dinger方程起着重要的作用.我们重点关注该系统有限时间内的存在性和性态,并导出了该系统解爆破的一个显示精确门槛标准.进一步,证明了该系统径对称爆破解的集中性.  相似文献   

14.
梁霄  Harish BHATT 《数学学报》2019,62(4):663-672
本文针对时空分数阶非线性薛定谔方程,提出了应用Padé近似逼近Mittag-Leffler函数的指数时间差分格式,讨论了提高格式计算效率的方法.本文在具有各种参数的时空分数阶非线性薛定谔方程上进行了数值实验,实验结果说明了所提出方法的准确性、有效性和可靠性.  相似文献   

15.
Let L be a Schr?dinger operator of the form L =-Δ + V acting on L~2(R~n) where the nonnegative potential V belongs to the reverse H?lder class B_q for some q ≥ n. In this article we will show that a function f ∈ L~(2,λ)(R~n), 0 λ n, is the trace of the solution of L_u =-u_(tt) + L_u =0, u(x, 0) = f(x), where u satisfies a Carleson type condition sup x_B,r_Br_B~(-λ)∫_0~(rB)∫_(B(x_B,r_B))t|u(x,t)|~2dxdt≤C∞.Its proof heavily relies on investigate the intrinsic relationship between the classical Morrey spaces and the new Campanato spaces L_L~(2,λ)(R~n) associated to the operator L, i.e.L_L~(2,λ)(R~n)=L~(2,λ)(R~n).Conversely, this Carleson type condition characterizes all the L-harmonic functions whose traces belong to the space L~(2,λ)(R~n) for all 0 λ n.  相似文献   

16.
In this paper,we study the scattering and blow-up dichotomy result of the radial solution to nonlinear Schrodinger equation(NLS) with the combined terms iu_t+△u=-|u|~4u+|4|~(p-1)u,1+4/3p5 in energy space H~1(R~3).The threshold energy is the energy of the ground state W of the focusing,energy critical NLS,which means that the subcritical perturbation does not affect the determination of threshold,but affects the scattering and blow-up dichotomy result with subcritical threshold energy.This extends algebraic perturbation in a previous work of Miao,Xu and Zhao[Comm.Math.Phys.,318,767-808(2013)]to all mass supercritical,energy subcritical perturbation.  相似文献   

17.
This paper is concerned with one-dimensional derivative quintic nonlinear Schrodinger equation,iut—uxx+i(|u|4u)x=0,x eT.The existence of a large amount of quasi-periodic solutions with two frequencies for this equation is established.The proof is based on partial Birkhoff normal form technique and an unbounded KAM theorem.We mention that in the present paper the mean value of u does not need to be zero,but small enough,which is different from the assumption(1.7)in Geng-Wu[J.Math.Phys.、53,102702(2012)].  相似文献   

18.
In this work we shall consider the initial value problem associated to the generalized derivative Schrödinger (gDNLS) equations and Following the argument introduced by Cazenave and Naumkin we shall establish the local well-posedness for a class of small data in an appropriate weighted Sobolev space. The other main tools in the proof include the homogeneous and inhomogeneous versions of the Kato smoothing effect for the linear Schrödinger equation established by Kenig-Ponce-Vega.  相似文献   

19.
We study a quasilinear Schrödinger equation -εNΔNu+V(x)|u|N-2u=Q(x)f(u) in RN, 01,N(RN),u(x)0, where V, Q are two continuous real functions on RN and ε>0 is a real parameter. Assume that the nonlinearity f is of exponential critical growth in the sense of Trudinger-Moser inequality, we are able to establish the existence and concentration of the semiclassical solutions by variational methods.  相似文献   

20.
利用平均向量场方法(AVF)对非线性薛定谔方程进行求解, 在理论上得到了一个保非线性薛定谔方程描述的系统能量守恒的AVF格式, 再分别用非线性薛定谔方程的AVF格式和辛格式数值模拟孤立波的演化行为, 并比较两个格式是否保系统能量守恒特性. 数值结果表明, AVF格式也能很好地模拟孤立波的演化行为,并且比辛格式更能保持系统的能量守恒.  相似文献   

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