Results 51 to 60 of about 1,726 (89)

An estimate for the number of bound states of the Schrödinger operator in two dimensions [PDF]

, 2004
For the Schrödinger operator -Δ + V on R^2 be the number of bound states. One obtains the following estimate: N(V) ≤ 1 + ∫_(R^2)∫_(R^2)|V(x)|V(y)|C_(1)ln|x-y|+C_2|^2 dx dy where C_1 = -1/2π and C_2 = (ln2-γ)/2π (γ is the Euler constant).
Stoiciu, Mihai
core  

Separation of Coupled Systems of Schrodinger Equations by Darboux transformations

, 2011
Darboux transformations in one independent variable have found numerous applications in various field of mathematics and physics. In this paper we show that the extension of these transformations to two dimensions can be used to decouple systems of ...
Magri F., MAYER HUMI, Nabiev A. A., Rogers C.   +3 more
core   +1 more source

Sobolev inequality for localization of pseudo-relativistic energy [PDF]

arXiv, 2005
In this article we present Sobolev-type inequalities for the localization of pseudo-relativistic energy.
arxiv  

A Strichartz estimate for quasiperiodic functions [PDF]

arXiv, 2023
In this work we prove a Strichartz estimate for the Schr\"odinger equation in the quasiperiodic setting. We also show a lower bound on the number of resonant frequency interactions in this situation.
arxiv  

Concentration phenomena for a fractional relativistic Schrödinger equation with critical growth

Advances in Nonlinear Analysis
In this paper, we are concerned with the following fractional relativistic Schrödinger equation with critical growth: (−Δ+m2)su+V(εx)u=f(u)+u2s*−1inRN,u∈Hs(RN),u>0inRN,\left\{\begin{array}{ll}{\left(-\Delta +{m}^{2})}^{s}u+V\left(\varepsilon x)u=f\left(u)
Ambrosio Vincenzo
doaj   +1 more source

Fourth-order Schr\"odinger type operator with singular potentials

, 2016
In this paper we study the biharmonic operator perturbed by an inverse fourth-order potential. In particular, we consider the operator $A=\Delta^2-V=\Delta^2-c|x|^{-4}$ where $c$ is any constant such that ...
Gregorio, Federica, Mildner, Sebastian
core   +1 more source

On the Schrodinger maximal function in higher dimension [PDF]

arXiv, 2012
New estimates on the maximal function associated to the linear Schrodinger equation are ...
arxiv  

Weighted Hessian estimates in Orlicz spaces for nondivergence elliptic operators with certain potentials [PDF]

arXiv, 2023
We prove interior weighted Hessian estimates in Orlicz spaces for nondivergence type elliptic equations with a lower order term which involves a nonnegative potential satisfying a reverse H\"older type condition.
arxiv  

On the p-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity

Demonstratio Mathematica
In this article, we deal with the following pp-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity: M([u]s,Ap)(−Δ)p,Asu+V(x)∣u∣p−2u=λ∫RN∣u∣pμ,s*∣x−y∣μdy∣u∣pμ,s*−2u+k∣u∣q−2u,x∈RN,M({\left[u]}
Zhao Min, Song Yueqiang, Repovš Dušan D.   +2 more
doaj   +1 more source

Pauli operators and the d-bar-Neumann problem [PDF]

arXiv, 2017
We apply methods from complex analysis, in particular the d-bar-Neumann operator, to investigate spectral properties of Pauli operators.
arxiv