Results 91 to 100 of about 1,829 (110)

A counterexample to an endpoint bilinear Strichartz inequality

, 2006
The endpoint Strichartz estimate $\| e^{it\Delta} f \|_{L^2_t L^\infty_x(\R \times \R^2)} \lesssim \|f\|_{L^2_x(\R^2)}$ is known to be false by the work of Montgomery-Smith, despite being only ``logarithmically far'' from being true in some sense.
Tao, Terence
core   +1 more source

Weak asymptotics for Schrodinger evolution [PDF]

arXiv, 2009
We apply technique developed in [2] to study the long-time behavior of Schrodinger evolution.
arxiv  

Compactness of the $\bar\partial $ - Neumann operator on weighted $(0,q)$- forms [PDF]

arXiv, 2010
As an application of a new characterization of compactness of the $\bar\partial $-Neumann operator we derive a sufficient condition for compactness of the $\bar\partial $- Neumann operator on $(0,q)$-forms in weighted $L^2$-spaces on $\mathbb{C}^n.$
arxiv  

The Schroedinger Equation with Potential in Random Motion [PDF]

arXiv, 2011
We study Schroedinger's equation with a potential moving along a Brownian motion path. We prove a RAGE-type theorem and Strichartz estimates for the solution on average.
arxiv  

Negative eigenvalues of two-dimensional Schrödinger operators [PDF]

arXiv, 2011
We prove a certain upper bound for the number of negative eigenvalues of the Schr\"{o}dinger operator on the plane.
arxiv  

Explicit formulas for the Schroedinger wave operators in R^2

, 2012
In this note, we derive explicit formulas for the Schroedinger wave operators in R^2 under the assumption that 0-energy is neither an eigenvalue nor a resonance.
de Aldecoa, R. Tiedra, Richard, S.
core   +1 more source

Existence of ground states to quasi-linear Schrödinger equations with critical exponential growth involving different potentials

Advanced Nonlinear Studies
The purpose of this paper is three-fold. First, we establish singular Trudinger–Moser inequalities with less restrictive constraint:(0.1)supu∈H1(R2),∫R2(|∇u|2+V(x)u2)dx≤1∫R2e4π1−β2u2−1|x ...
Zhang Caifeng, Zhu Maochun
doaj   +1 more source

Existence and properties of soliton solution for the quasilinear Schrödinger system

Open Mathematics
In this article, we consider the following quasilinear Schrödinger system: −εΔu+u+k2ε[Δ∣u∣2]u=2αα+β∣u∣α−2u∣v∣β,x∈RN,−εΔv+v+k2ε[Δ∣v∣2]v=2βα+β∣u∣α∣v∣β−2v,x∈RN,\left\{\begin{array}{ll}-\varepsilon \Delta u+u+\frac{k}{2}\varepsilon \left[\Delta \hspace{-0 ...
Zhang Xue, Zhang Jing
doaj   +1 more source

A class of pseudo-differential operators with oscillating symbols [PDF]

arXiv, 1998
We study a class of pseudo-differential operators with oscillating symbols or osc illating amplitudes appearing in the long-range scattering theory. We develop the basic calc ulus for operators from such classes and solve some concrete problems posed by applications to scattering theory, especially to the scattering matrix. In particular, we show tha t
arxiv  

Semi-classical analysis of Schrodinger operators and compactness in the d-bar-Neumann problem [PDF]

arXiv, 2002
We study the asymptotic behavior, in a ``semi-classical limit'', of the first eigenvalues (i.e. the groundstate energies) of a class of Schr\"{o}dinger operators with magnetic fields and the relationship of this behavior with compactness in the $\bar\partial$-Neumann problem on Hartogs domains in $\C^2$
arxiv