共查询到20条相似文献，搜索用时 31 毫秒
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E. Grenier 《Proceedings of the American Mathematical Society》1998,126(2):523-530
We study the semi-classical limit of the nonlinear Schrödinger equation for initial data with Sobolev regularity, before shocks appear in the limit system, and in particular the validity of the WKB method.
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Yanheng Ding 《Proceedings of the American Mathematical Society》2002,130(3):689-696
We establish existence and multiplicity of solutions to a class of nonlinear Schrödinger equations with, e.g., ``atomic' Hamiltonians, via critical point theory.
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In this paper, we show that any solution of the nonlinear Schrödinger equation which blows up in finite time, satisfies a mass concentration phenomena near the blow-up time. Our proof is essentially based on Bourgain's (1998), which has established this result in the bidimensional spatial case, and on a generalization of Strichartz's inequality, where the bidimensional spatial case was proved by Moyua, Vargas and Vega (1999). We also generalize to higher dimensions the results in Keraani (2006) and Merle and Vega (1998).
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本文讨论了在实轴上具有紧支集的势的薛定谔算子的极点散射问题. 本文旨在将狄利克雷级数理论与散射理论相结合, 文中运用了Littlewood的经典方法得到关于极点个数的新的估计. 本文首次将狄利克雷级数方法用于极点估计, 由此得到了极点个数的上界与下界, 这些结果改进和推广了该论题的一些相关结论. 相似文献
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J. Bourgain 《Journal of the American Mathematical Society》1999,12(1):145-171
We establish global wellposedness and scattering for the -critical defocusing NLS in 3D
assuming radial data , . In particular, it proves global existence of classical solutions in the radial case. The same result is obtained in 4D for the equation
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Alexei Rybkin 《Proceedings of the American Mathematical Society》2002,130(1):59-67
For the general one dimensional Schrödinger operator with real we present a complete streamlined treatment of large spectral parameter power asymptotics of Jost solutions and the scattering matrix. We find simple necessary and sufficient conditions relating the number of exact terms in the asymptotics with the smoothness of . These conditions are expressed in terms of the Fourier transform of some functions related to . In particular, under the usual conditions we derive up to two extra terms in the asymptotic expansion of the Jost solution and for the transmission coefficient we derive twice as many terms. Our main results are complete.
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Vladimir Georgiev Angel Ivanov 《Proceedings of the American Mathematical Society》2005,133(7):1993-2003
We consider the Schrödinger equation in three-dimensional space with small potential in the Lorentz space and we prove Strichartz-type estimates for the solution to this equation. Moreover, using Cook's method, we prove the existence of the wave operator. In the last section we prove the equivalence between the homogeneous Sobolev spaces and in the case .
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Wojciech Czaja Jacek Zienkiewicz 《Proceedings of the American Mathematical Society》2008,136(1):89-94
Given a Schrödinger operator on with nonnegative potential , we present an atomic characterization of the associated Hardy space .
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乔蕾 《数学年刊A辑(中文版)》2016,37(3):303-310
给出了锥中稳态Schr\"{o}dinger方程解的Liouville型定理,推广了邓冠铁在半空间中关于拉普拉斯方程解的相关结论. 相似文献
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In this paper, Strichartz estimates for the solution of the Schrödinger evolution equation are considered on a mixed normed space with Lorentz norm with respect to the time variable.
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In this paper, the authors investigate the sharp threshold of a three-dimensional nonlocal nonlinear Schr¨odinger system. It is a coupled system which provides the mathematical modeling of the spontaneous generation of a magnetic field in a cold plasma under the subsonic limit. The main difficulty of the proof lies in exploring the inner structure of the system due to the fact that the nonlocal effect may bring some hinderance for establishing the conservation quantities of the mass and of the energy, constructing the corresponding variational structure, and deriving the key estimates to gain the expected result. To overcome this, the authors must establish local well-posedness theory, and set up suitable variational structure depending crucially on the inner structure of the system under study, which leads to define proper functionals and a constrained variational problem. By building up two invariant manifolds and then making a priori estimates for these nonlocal terms, the authors figure out a sharp threshold of global existence for the system under consideration. 相似文献
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In this paper, we consider the Cauchy problem for the nonlinear Schr\"{o}dinger equation with combined power-type nonlinearities, which is mass-critical/supercr-itical, and energy-subcritical. Combing Du, Wu and Zhang'' argument with the variational method, we prove that if the energy of the initial data is negative (or under some more general condition), then the $H^1$-norm of the solution to the Cauchy problem will go to infinity in some finite time or infinite time. 相似文献
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This paper concerns the rate of -concentration of the blow-up solutions for the critical nonlinear Schrödinger equation. The result of Tsutsumi is improved in terms of Merle and Raphaël's recent arguments.
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This paper deals with semilinear elliptic equations in an exterior domain of with . Sufficient conditions are obtained for the equation to have a positive solution which decays at infinity. The main result is proved by means of a supersolution-subsolution method presented by Noussair and Swanson. By using phase plane analysis of a system of Liénard type, a suitable positive supersolution is found out. Asymptotic decay estimation on a solution of the Liénard system gains a positive subsolution. Examples are given to illustrate the main result.
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Alexei Rybkin 《Proceedings of the American Mathematical Society》2003,131(1):219-229
For the general one dimensional Schrödinger operator with real we study some analytic aspects related to order-one trace formulas originally due to Buslaev-Faddeev, Faddeev-Zakharov, and Gesztesy-Holden-Simon-Zhao. We show that the condition guarantees the existence of the trace formulas of order one only with certain resolvent regularizations of the integrals involved. Our principle results are simple necessary and sufficient conditions on absolute summability of the formulas under consideration. These conditions are expressed in terms of Fourier transforms related to .
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In this paper we show that a positive superfunction on a cone behaves regularly at infinity outside a minimally thin set associated with the stationary Schr(o|¨)dinger operator. 相似文献
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In this paper, we investigate the controllability of 1D bilinear Schr\"{o}dinger equation with Sturm-Liouville boundary value condition. The system represents a quantumn particle controlled by an electric field. K. Beauchard and C. Laurent have proved local controllability of 1D bilinear Schr\"{o}dinger equation with Dirichlet boundary value condition in some suitable Sobolev space based on the classical inverse mapping theorem. Using a similar method, we extend this result to Sturm-Liouville boundary value proplems. 相似文献
