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On a method of two-sided eigenvalue estimates for elliptic equations of the form $A u - λ B u = 0$

Karel Rektorys, Zdeněk Vospěl (1981)

Aplikace matematiky

The Collatz method of twosided eigenvalue estimates was extended by K. Rektorys in his monography Variational Methods to the case of differential equations of the form $A u - λ B u = 0$ with elliptic operators. This method requires to solve, successively, certain boundary value problems. In the case of partial differential equations, these problems are to be solved approximately, as a rule, and this is the source of further errors. In the work, it is shown how to estimate these additional errors, or how to avoid...

On an estimate for the principal eigenvalue of a linear elliptic problem

Gossez, Jean-Pierre, Lami Dozo, Enrique (1982)

Portugaliae mathematica

On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

De Schepper, H. (2000)

Serdica Mathematical Journal

We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is...

On Higher Riesz Transforms for Gaussian Measures.

C.E. Gutiérrez, C. Segovia (1995)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

On Non-Degeneracy of the Ground State of Schrödinger Operators.

Heinz-Willi Goelden (1977)

Mathematische Zeitschrift

On Positive Solutions of a Linear Elliptic Eigenvalue Problem with Neumann Boundary Conditions.

Peter Hess, Stefan Senn (1981)

Mathematische Annalen

On Selberg's Eigenvalue Conjecture.

P. Sarnak, W. Luo, Z. Rudnick (1995)

Geometric and functional analysis

On some linear eigenvalue problems for strongly elliptic systems with an indefinite weight matrix function

Jan Bochenek (1989)

Annales Polonici Mathematici

On some new spectral estimates for Schrödinger-like operators

Daniel Levin (2006)

Open Mathematics

We prove the analog of the Cwikel-Lieb-Rozenblum estimate for a wide class of second-order elliptic operators by two different tools: Lieb-Thirring inequalities for Schrödinger operators with matrix-valued potentials and Sobolev inequalities for warped product spaces.

On spectral approximation. Part 1. The problem of convergence

Jean Descloux, Nabil Nassif, Jacques Rappaz (1978)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

On spectral approximation. Part 2. Error estimates for the Galerkin method

Jean Descloux, Nabil Nassif, Jacques Rappaz (1978)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

On the approximation of the spectrum of the Stokes operator

Tunc Geveci, B. Daya Reddy, Howard T. Pearce (1989)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

On the asymptotic distribution of the eigenvalue branches of the Schrödinger operator H... W in a spectral gap of H.

Rainer Hempel (1989)

Journal für die reine und angewandte Mathematik

On the Bethe-Sommerfeld conjecture

Leonid Parnovski, Alexander V. Sobolev (2000)

Journées équations aux dérivées partielles

We consider the operator in $ℝ^{d}, d \geq 2$ , of the form $H = {(- Δ)}^{l} + V, l > 0$ with a function $V$ periodic with respect to a lattice in $ℝ^{d}$ . We prove that the number of gaps in the spectrum of $H$ is finite if $8 l > d + 3$ . Previously the finiteness of the number of gaps was known for $4 l > d + 1$ . Various approaches to this problem are discussed.

On the convergence of eigenvalues for mixed formulations

Daniele Boffi, Franco Brezzi, Lucia Gastaldi (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On the eigenvalue asymptotics of certain Schrödinger operators

Wiesław Cupała (1993)

Studia Mathematica

Subelliptic estimates on nilpotent Lie groups and the Cwikel-Lieb-Rosenblum inequality are used to estimate the number of eigenvalues for Schrödinger operators with polynomial potentials.

On the eigenvalues of a Robin problem with a large parameter

Alexey Filinovskiy (2014)

Mathematica Bohemica

We consider the Robin eigenvalue problem $Δ u + λ u = 0$ in $Ω$ , $\partial u / \partial ν + α u = 0$ on $\partial Ω$ where $Ω \subset ℝ^{n}$ , $n \geq 2$ is a bounded domain and $α$ is a real parameter. We investigate the behavior of the eigenvalues $λ_{k} (α)$ of this problem as functions of the parameter $α$ . We analyze the monotonicity and convexity properties of the eigenvalues and give a variational proof of the formula for the derivative $λ_{1}^{'} (α)$ . Assuming that the boundary $\partial Ω$ is of class $C^{2}$ we obtain estimates to the difference $λ_{k}^{D} - λ_{k} (α)$ between the $k$ -th eigenvalue of the Laplace operator with Dirichlet...

On the essential spectrum of many-particle pseudorelativistic Hamiltonians with permutational symmetry account.

Zhislin, Grigorii (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

On the existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems.

Jacqueline Fleckinger, Jesús Hernández, François De Thélin (2003)

RACSAM

We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the inverse of the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.

On the First Eigenvalue of Non-Uniformly Elliptic Boundary Value Problems.

Neil S. Trudinger (1980)

Mathematische Zeitschrift

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