On the number of negative eigenvalues of an elliptic operator

DOI10.1016/j.bulsci.2012.10.005zbMath1286.35178OpenAlexW1966794158MaRDI QIDQ388128

Mohammed El Aïdi

Publication date: 19 December 2013

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2012.10.005

zbMATH Keywords

Robin boundary conditionselliptic operatoreigenvalue boundsCourant minimax principle

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Estimates of eigenvalues in context of PDEs (35P15) Eigenvalue problems for linear operators (47A75) General theory of partial differential operators (47F05)

Related Items (3)

A weighted Hardy type inequality and its applications ⋮ An explicit upper bound of the number of negative eigenvalues associated to an elliptic operator ⋮ A lower bound for the number of negative eigenvalues on a Euclidean space and on a complete Riemannian manifold

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Un majorant du nombre des valeurs propres négatives correspondantes à l'opérateur de Schrödinger généralisé.
• A remark on two dimensional periodic potentials
• Resonance scattering on a negative potential
• The trace inequality and eigenvalue estimates for Schrödinger operators
• Asymptotic formulas for the eigenvalues of a periodic Schrödinger operator and the Bethe-Sommerfeld conjecture
• The mathematical theory of resonances whose widths are exponentially small
• Resonances in Born-Oppenheimer approximation. II: Length of resonances.
• Résonances dans l'approximation de Born-Oppenheimer. I. (Resonances in Born-Oppenheimer approximation. I)
• Partial differential equations I. Foundations of the classical theory. Transl. from the Russian by R. Cooke
• The negative discrete spectrum of the operator \((-\Delta)^ l-\alpha V\) in \(L_ 2(\mathbb{R}^ d)\) for \(d\) even and \(2l\geq d\)
• Asymptotic distribution of resonances in one dimension
• Resonance expansions of propagators in the presence of potential barriers.
• On the Bethe-Sommerfeld conjecture for the polyharmonic operator.
• On spectral theory of elliptic operators
• Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory
• The uncertainty principle
• Résonances en limite semi-classique
• Estimates of the negative spectrum of an elliptic operator
• Bounds on the eigenvalues of the Laplace and Schroedinger operators
• Upper Bounds for the Resonance Counting Function of Schrödinger Operators in Odd Dimensions
• Sur les resonances de l'operateur de dirichlet dans un tube
• Existence of resonances in potential scattering
• Sobolev Spaces
• Perturbation theory for the Schrödinger operator with a periodic potential
• Negative spectrum of an elliptic operator with Robin boundary conditions

This page was built for publication: On the number of negative eigenvalues of an elliptic operator