Results 51 to 60 of about 1,721 (102)

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  

Elementary linear algebra for advanced spectral problems [PDF]

arXiv, 2003
We discuss the general method of Grushin problems, closely related to Shur complements, Feshbach projections and effective Hamiltonians, and describe various appearances in spectral theory, pdes, mathematical physics and numerical problems.
arxiv  

On the number of nodal domains of the 2D isotropic quantum harmonic oscillator -- an extension of results of A. Stern -- [PDF]

, 2014
In the case of the sphere and the square, Antonie Stern (1925) claimed in her PhD thesis the existence of an infinite sequence of eigenvalues whose corresponding eigenspaces contain an eigenfunction with two nodal domains. These two statements were given
Bérard, Pierre, Helffer, Bernard
core   +3 more sources

On multiplicity of solutions to nonlinear Dirac equation with local super-quadratic growth

Advances in Nonlinear Analysis
In this article, we study the following nonlinear Dirac equation: −iα⋅∇u+aβu+V(x)u=g(x,∣u∣)u,x∈R3.-i\alpha \hspace{0.33em}\cdot \hspace{0.33em}\nabla u+a\beta u+V\left(x)u=g\left(x,| u| )u,\hspace{1em}x\in {{\mathbb{R}}}^{3}.
Liao Fangfang, Chen Tiantian
doaj   +1 more source

Dispersive estimates for the three-dimensional Schroedinger equation with rough potentials [PDF]

Amer. J. Math. 128 (2006) 731-750., 2004
We prove L^1 --> L^\infty estimates for the linear Schroedinger equation in three dimensions. The potential is assumed to belong to certain L^p spaces, but no pointwise decay estimates and no additional regularity is required.
arxiv  

Dispersive estimates for Schroedinger operators: A survey [PDF]

arXiv, 2005
We present some old and new results on dispersive estimates for Schroedinger equations.
arxiv  

Solutions for Toda systems on Riemann surfaces [PDF]

arXiv, 2005
In this paper, we study the solutions of Toda systems on Riemann surface in the critical case, we prove a sufficient condition for the existence of solutions of Toda systems.
arxiv  

The Kato smoothing effect for Schr{ö}dinger equations with unbounded potentials in exterior domains [PDF]

arXiv, 2006
In this paper we prove the smoothing effect for solutions of Schr{\"o}dinger equations with variable coefficients and in a non trapping exterior domain. We allow quadratic potentials at infinity.
arxiv  

Analyticity of the density of electronic wavefunctions [PDF]

Ark. Math. 42 (2004), 87-106, 2002
We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in ${\mathbb R}^3$ away from the nuclei.
arxiv  

Microlocal smoothing effect for the Schrödinger evolution equation in a Gevrey class [PDF]

arXiv, 2008
We discuss the microlocal Gevrey smoothing effect for the Schr\"odinger equation with variable coefficients via the propagation property of the wave front set of homogenous type. We apply the microlocal exponential estimates in a Gevrey case to prove our result.
arxiv