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Local energy decay for several evolution equations on asymptotically euclidean manifolds

Jean-François Bony, Dietrich Häfner (2012)

Annales scientifiques de l'École Normale Supérieure

Let $P$ be a long range metric perturbation of the Euclidean Laplacian on $ℝ^{d}$ , $d \geq 2$ . We prove local energy decay for the solutions of the wave, Klein-Gordon and Schrödinger equations associated to $P$ . The problem is decomposed in a low and high frequency analysis. For the high energy part, we assume a non trapping condition. For low (resp. high) frequencies we obtain a general result about the local energy decay for the group $e^{i t f (P)}$ where $f$ has a suitable development at zero (resp. infinity).

Local energy decay for waves governed by a system of nonlinear Schrödinger equations in a nonuniform medium.

Lin, J.E. (1985)

International Journal of Mathematics and Mathematical Sciences

Local properties of stationary solutions of some nonlinear singular Schrödinger equations.

Bouchaib Guerch, Laurent Véron (1991)

Revista Matemática Iberoamericana

We study the local behaviour of solutions of the following type of equation,-Δu - V(x)u + g(u) = 0 when V is singular at some points and g is a non-decreasing function. Emphasis is put on the case when V(x) = c|x|-2 and g has a power-like growth.

Local Time-Decay of High Energy Scattering States for the Schrödinger Equation.

Hans L. Cycon, Perry Peter A. (1984/1985)

Mathematische Zeitschrift

Location of resonances generated by degenerate potential barrier.

Baklouti, Hamadi, Mnif, Maher (2006)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Lower bounds for pseudo-differential operators

N. Lerner, J. Nourrigat (1989/1990)

Séminaire Équations aux dérivées partielles (Polytechnique)

Lower bounds for pseudo-differential operators

Nicolas Lerner, Jean Nourrigat (1990)

Annales de l'institut Fourier

This paper contains some new results on lower bounds for pseudo-differential operators whose symbols do not remain positive. Non-negativity of averages of the symbol on canonical images of the unit ball is sufficient to get a Gårding type inequality for Schrödinger operators with magnetic potential and one dimensional pseudo-differential operators.

Lower bounds for Schrödinger equations

Charles Fefferman, D. H. Phong (1982)

Journées équations aux dérivées partielles

Lower bounds for Schrödinger operators in H¹(ℝ)

Ronan Pouliquen (1999)

Studia Mathematica

We prove trace inequalities of type $| | u^{'} {| |}_{L^{2}}^{2} + \sum_{j \in ℤ} k_{j} | u (a_{j}) |^{2} {\geq λ | | u | |}_{L^{2}}^{2}$ where $u \in H^{1} (ℝ)$ , under suitable hypotheses on the sequences ${a_{j}}_{j \in ℤ}$ and ${k_{j}}_{j \in ℤ}$ , with the first sequence increasing and the second bounded.

Lower bounds for the infimum of the spectrum of the Schrödinger operator in $ℝ^{N}$ and the Sobolev inequalities.

Veling, E. J. M. (2002)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Magnetic barriers of compact support and eigenvalues in spectral gaps.

Hempel, Reiner, Besch, Alexander (2003)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Magnetic Schrödinger Operator: Geometry, Classical and Quantum Dynamics and Spectral Asymptotics

Victor Ivrii (2006/2007)

Séminaire Équations aux dérivées partielles

I study the Schrödinger operator with the strong magnetic field, considering links between geometry of magnetic field, classical and quantum dynamics associated with operator and spectral asymptotics. In particular, I will discuss the role of short periodic trajectories.

Majoration de multiplicité pour l'opérateur de Schrödinger

Colette Anné (1989/1990)

Séminaire de théorie spectrale et géométrie

Martin boundary for Schrödinger operators with singularity.

W. Hansen, A. Boukricha (1994)

Mathematische Annalen

Martin compactification and asymptotics of Green functions for Schrödinger operators with anisotropic potentials.

Minoru Murata (1990)

Mathematische Annalen

Matrices de diffusion pour l'opérateur de Schrödinger avec champ magnétique et phénomène de Aharonov-Bohm

François Nicoleau (1993)

Journées équations aux dérivées partielles

Maximal inequalities and Riesz transform estimates on $L^{p}$ spaces for Schrödinger operators with nonnegative potentials

Pascal Auscher, Besma Ben Ali (2007)

Annales de l’institut Fourier

We show various $L^{p}$ estimates for Schrödinger operators $- Δ + V$ on $ℝ^{n}$ and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen. Our main tools are improved Fefferman-Phong inequalities and reverse Hölder estimates for weak solutions of $- Δ + V$ and their gradients.

Moyenne de formes quadratiques positives et champs magnétiques

Alain Dufresnoy (1984/1985)

Séminaire de théorie spectrale et géométrie

Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields

Huirong Pi, Chunhua Wang (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we are concerned with the existence of multi-bump solutions for a nonlinear Schrödinger equations with electromagnetic fields. We prove under some suitable conditions that for any positive integer m, there exists ε(m) > 0 such that, for 0 < ε < ε(m), the problem has an m-bump complex-valued solution. As a result, when ε → 0, the equation has more and more multi-bump complex-valued solutions.

Multidimensional two-particles problem with non-central potential

D. V. Choodnovsky, G. V. Choodnovsky (1977/1978)

Séminaire sur les équations non linéaires (Choodnovsky)

Currently displaying 201 – 220 of 591

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