共查询到20条相似文献,搜索用时 15 毫秒
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利用隐式守恒型差分格式来离散空间分数阶非线性薛定谔方程,可得到一个离散线性方程组.该离散线性方程组的系数矩阵为一个纯虚数复标量矩阵、一个对角矩阵与一个对称Toeplitz矩阵之和.基于此,本文提出了用一种\textit{修正的埃尔米特和反埃尔米特分裂}(MHSS)型迭代方法来求解此离散线性方程组.理论分析表明,MHSS型迭代方法是无条件收敛的.数值实验也说明了该方法是可行且有效的. 相似文献
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Zbigniew Leśniak 《Journal of Difference Equations and Applications》2016,22(7):853-864
We prove that the set of all regular points of a flow of Brouwer homeomorphisms is invariant under topological equivalence of flows. We also show that a similar result holds for the first prolongational limit set. 相似文献
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We prove the global existence and scattering for the Hartree-type equation in H s (?3) the low regularity space s < 1. We follow the ideas in Colliander et al. (2004) to the Hartree-type nonlinearity, and also develop the theory of the classical multilinear operator modifying the L p estimate in Coifman and Meyer (1978). 相似文献
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Hisao Kato 《Transactions of the American Mathematical Society》1997,349(9):3645-3655
A homeomorphism of a compactum with metric is expansive if there is such that if and , then there is an integer such that . It is well-known that -adic solenoids () admit expansive homeomorphisms, each is an indecomposable continuum, and cannot be embedded into the plane. In case of plane continua, the following interesting problem remains open: For each , does there exist a plane continuum so that admits an expansive homeomorphism and separates the plane into components? For the case , the typical plane continua are circle-like continua, and every decomposable circle-like continuum can be embedded into the plane. Naturally, one may ask the following question: Does there exist a decomposable circle-like continuum admitting expansive homeomorphisms? In this paper, we prove that a class of continua, which contains all chainable continua, some continuous curves of pseudo-arcs constructed by W. Lewis and all decomposable circle-like continua, admits no expansive homeomorphisms. In particular, any decomposable circle-like continuum admits no expansive homeomorphism. Also, we show that if is an expansive homeomorphism of a circle-like continuum , then is itself weakly chaotic in the sense of Devaney.
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Beverly Brechner 《Topology and its Applications》1980,11(3):231-242
A homeomorphism of Rn onto itself is called positively regular (or EC+) iff its family of non-negative iterates is pointwise equicontinuous. For EC+ homeomorphism of Rn such that some point of Rn has bounded positive semi-orbit, the nucleus M is defined, and the following theorems are proved.Theorem 1. If such a homeomorphism h:Rn→Rn has compact nucleus M, then M is a fully invariant compact AR. Further, for n≠4,5,h:Rn/M→Rn/M is conjugate to a contraction on Rn.Theorem 2. In Rn,n≠4,5,M compact iff there existsa disk D such that h(D)?IntD.Theorem 3. In R2, either M is a disk and h|M is a rotation, or h|M is periodic. The relationship between M and the irregular set of ? is also studied. 相似文献
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AMS(MOS): 65L10 The convergence of the discrete Green's function gh is studied for finite difference schemes approximating m-th order linear two-point boundary value problems. Schemes of noncompact form and in part of the paper also nonuniform grids are admitted. Sharp convergence results are obtained for the difference quotients of gh up to order m-1. 相似文献
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We study persistent properties of solutions of the semi-linear Schrödinger equations in weighted spaces. 相似文献
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Cristóbal J. Meroño 《Journal of Differential Equations》2019,266(10):6307-6345
We prove that in dimension the main singularities of a complex potential q having a certain a priori regularity are contained in the Born approximation constructed from backscattering data. This is archived using a new explicit formula for the multiple dispersion operators in the Fourier transform side. We also show that can be up to one derivative more regular than q in the Sobolev scale. On the other hand, we construct counterexamples showing that in general it is not possible to have more than one derivative gain, sometimes even strictly less, depending on the a priori regularity of q. 相似文献
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This paper deals with the following slightly subcritical Schrödinger equation: where is a nonnegative smooth function, , , , . Most of the previous works for the Schrödinger equations were mainly investigated for power-type nonlinearity. In this paper, we will study the case when the nonlinearity is a non-power nonlinearity. We show that, for ε small enough, there exists a family of single-peak solutions concentrating at the positive stable critical point of the potential . 相似文献
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Gilson M. de Carvalho Rodrigo G. Clemente José Carlos de Albuquerque 《Mathematische Nachrichten》2023,296(9):4357-4373
We establish the existence of nontrivial solutions for the following class of quasilinear Schrödinger equations: where κ is a positive parameter, and are continuous functions that can be singular at the origin, unbounded or vanishing at infinity, and the nonlinearity has critical exponential growth motivated by the Trudinger–Moser inequality. To prove our main result, we apply variational methods together with careful -estimates. 相似文献
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《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(6):1739-1762
We prove a quantitative and global in time semiclassical limit from the Hartree to the Vlasov equation in the case of a singular interaction potential in dimension , including the case of a Coulomb singularity in dimension . This result holds for initial data concentrated enough in the sense that some space moments are initially sufficiently small. As an intermediate result, we also obtain quantitative bounds on the space and velocity moments of even order and the asymptotic behavior of the spatial density due to dispersion effects, uniform in the Planck constant ħ. 相似文献
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Zhouxin Li 《Journal of Differential Equations》2019,266(11):7264-7290
We prove the existence of positive solutions of the following singular quasilinear Schrödinger equations at critical growth via variational methods, where , , , , . It is interesting that we do not need to add a weight function to control . 相似文献
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Justin Holmer 《偏微分方程通讯》2013,38(5):878-905
We consider solutions u(t) to the 3d NLS equation i? t u + Δu + |u|2 u = 0 such that ‖xu(t)‖ L 2 = ∞ and u(t) is nonradial. Denoting by M[u] and E[u], the mass and energy, respectively, of a solution u, and by Q(x) the ground state solution to ?Q + ΔQ + |Q|2 Q = 0, we prove the following: if M[u]E[u] < M[Q]E[Q] and ‖u 0‖ L 2 ‖?u 0‖ L 2 > ‖Q‖ L 2 ‖?Q‖ L 2 , then either u(t) blows-up in finite positive time or u(t) exists globally for all positive time and there exists a sequence of times t n → + ∞ such that ‖?u(t n )‖ L 2 → ∞. Similar statements hold for negative time. 相似文献
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