相关论文: On minimal support properties of solutions of Schr…
In this work we shall review some of our recent results concerning unique continuation properties of solutions of Schr\"odinger equations. In this equations we include linear ones with a time depending potential and semi-linear ones.
We investigate unique continuation inequalities for solutions of the Schr\"odinger equations associated with special Hermite operators. Our main result establishes that if the solution remains small at two distinct time points outside sets…
Consider the Schrodinger equation -\Delta u =(k+V) u in an infinite slab S= \R^{n-1}x (0,1), where V is a bounded potential supported on a set D of finite measure. We prove necessary conditions for the existence of nontrivial admissible…
We consider a number of linear and non-linear boundary value problems involving generalized Schr\"odinger equations. The model case is $-\Delta u=Vu$ for $u\in W_0^{1,2}(D)$ with $D$ a bounded domain in ${\bf R^n}$. We use the Sobolev…
Schr\"odinger operators with potentials generated by primitive substitutions are simple models for one dimensional quasi-crystals. We review recent results on their spectral properties. These include in particular an algorithmically…
Using Carleman estimates, we give a lower bound for solutions to the discrete Schr\"odinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions.
In this paper we continue the study of the spectral gap of Schr\"odinger operators on large intervals and subject to Neumann boundary conditions. The main goal is to derive a lower bound on the spectral gap which is polynomial in the…
We present some lower bounds for regular solutions of Schr\"odinger equations with bounded and time dependent complex potentials. Assuming that the solution has some positive mass at time zero within a ball of certain radius, we prove that…
Estimates for the total multiplicity of eigenvalues for Schr\"odinger operator are established in the case of compactly supported or exponentially decreasing complex-valued potential.
In this paper we give new estimates for the solution to the Schr\"odinger equation with quadratic and sub-quadratic potentials in the framework of modulation spaces.
In this paper, we investigate quantitative propagation of smallness properties for the Schr\"odinger operator on a bounded domain in $\mathbb R^d$. We extend Logunov, Malinnikova's results concerning propagation of smallness for…
Given a potential $V$ and the associated Schr\"odinger operator $-\Delta+V$, we consider the problem of providing sharp upper and lower bound on the energy of the operator. It is known that if for example $V$ or $V^{-1}$ enjoys suitable…
By the multiple-scale method some new approximate absorbing boundary conditions for the Schr\"odinger type equations are obtained.
In this paper we give an estimate for the solution to the Schr\"odinger equation with sub-quadratic potentials in modulation spaces by the norm of the initial functions in Wiener-Amalgum spaces.
The main goal of this paper is to study the nature of the support of the solution of suitable nonlinear Schr\"{o}dinger equations mainly the compactness of the support and its spatial localization. This question is very related with pure…
In this paper we are concerned with nonlinear Schr\"odinger equations with random potentials. Our class includes continuum and discrete potentials. Conditions on the potential $V_{\omega}$ are found for existence of solutions almost sure…
In this paper we analyze the dispersion property of some models involving Schr\"odinger equations. First we focus on the discrete case and then we present some results on graphs.
In this paper, we extend our earlier unique continuation results \cite{PZ2} for the Schr\"odinger-type inequality $ |\bar\partial u| \le V|u|$ on a domain in $\mathbb C^n$ by removing the smoothness assumption on solutions $u = (u_1,…
In this paper, we intend to present some already known results about the internal controllability of the linear and nonlinear Schr\"odinger equation. After presenting the basic properties of the equation, we give a self contained proof of…
We find positive non-radial solutions for a system of Schr\"odinger equations in a weak fully attractive or repulsive regime in presence of an external radial trapping potential that exhibits a maximum or a minimum at infinity.