Obere Schranken für Eigenfunktionen eines Operators - ... + q.
Observability properties of a semi-discrete 1d wave equation derived from a mixed finite element method on nonuniform meshes
The goal of this article is to analyze the observability properties for a space semi-discrete approximation scheme derived from a mixed finite element method of the 1d wave equation on nonuniform meshes. More precisely, we prove that observability properties hold uniformly with respect to the mesh-size under some assumptions, which, roughly, measures the lack of uniformity of the meshes, thus extending the work [Castro and Micu, Numer. Math.102 (2006) 413–462] to nonuniform meshes. Our results...
On a Class of non Linear Schrödinger Equations with non Local Interaction.
On a magnetic characterization of spectral minimal partitions
Given a bounded open set in (or in a Riemannian manifold) and a partition of by open sets , we consider the quantity where is the ground state energy of the Dirichlet realization of the Laplacian in . If we denote by the infimum over all the -partitions of , a minimal -partition is then a partition which realizes the infimum. When , we find the two nodal domains of a second eigenfunction, but the analysis of higher ’s is non trivial and quite interesting. In this paper, we give...
On a method of two-sided eigenvalue estimates for elliptic equations of the form
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 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 a nonresonance condition between the first and the second eigenvalues for the -Laplacian.
On a priori estimates for positive solutions of a semilinear biharmonic equation in a ball
On a probabilistic interpretation of shape derivatives of Dirichlet groundstates with application to Fermion nodes
This paper considers Schrödinger operators, and presents a probabilistic interpretation of the variation (or shape derivative) of the Dirichlet groundstate energy when the associated domain is perturbed. This interpretation relies on the distribution on the boundary of a stopped random process with Feynman-Kac weights. Practical computations require in addition the explicit approximation of the normal derivative of the groundstate on the boundary. We then propose to use this formulation in the...
On a problem of lower limit in the study of nonresonance.
On a problem of lower limit in the study of nonresonance with Leray-Lions operator.
On a semilinear elliptic eigenvalue problem
We obtain a description of the spectrum and estimates for generalized positive solutions of -Δu = λ(f(x) + h(u)) in Ω, , where f(x) and h(u) satisfy minimal regularity assumptions.
On a Superlinear Elliptic Boundary Value Problem.
On an embedding criterion for interpolation spaces and application to indefinite spectral problems.
On an estimate for the principal eigenvalue of a linear elliptic problem
On an oblique derivative problem involving an indefinite weight
In this paper we derive results concerning the angular distrubition of the eigenvalues and the completeness of the principal vectors in certain function spaces for an oblique derivative problem involving an indefinite weight function for a second order elliptic operator defined in a bounded region.
On bifurcation intervals for nonlinear eigenvalue problems
We give a sufficient condition for [μ-M, μ+M] × {0} to be a bifurcation interval of the equation u = L(λu + F(u)), where L is a linear symmetric operator in a Hilbert space, μ ∈ r(L) is of odd multiplicity, and F is a nonlinear operator. This abstract result provides an elementary proof of the existence of bifurcation intervals for some eigenvalue problems with nondifferentiable nonlinearities. All the results obtained may be easily transferred to the case of bifurcation from infinity.
On counting the number of eigenvalues in the right half-plane for spectral problems connected with hyperbolic systems. II: Differential equations.
On Cramér's theorem for general Euler products with functional equation.
On diamagnetism and de Haas-van Alphen effect
On Dirichlet-Schrödinger operators with strong potentials
We consider Schrödinger operators H = -Δ/2 + V (V≥0 and locally bounded) with Dirichlet boundary conditions, on any open and connected subdomain which either is bounded or satisfies the condition as |x| → ∞. We prove exponential decay at the boundary of all the eigenfunctions of H whenever V diverges sufficiently fast at the boundary ∂D, in the sense that as . We also prove bounds from above and below for Tr(exp[-tH]), and in particular we give criterions for the finiteness of such trace....