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Semi-classical analysis and vanishing properties of solutions to quasilinear equations.

Belaud, Yves (2002)

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

Semiclassical resonances in some simple cases

Johannes Sjöstrand (1986)

Journées équations aux dérivées partielles

Semi-classical trace formula and clustering of eigenvalues for Schrödinger operators

Vesselin Petkov, Georgi Popov (1998)

Annales de l'I.H.P. Physique théorique

Sharp bounds for the intersection of nodal lines with certain curves

Junehyuk Jung (2014)

Journal of the European Mathematical Society

Let $Y$ be a hyperbolic surface and let $φ$ be a Laplacian eigenfunction having eigenvalue $- 1 / 4 - τ^{2}$ with $τ > 0$ . Let $N (φ)$ be the set of nodal lines of $φ$ . For a fixed analytic curve $γ$ of finite length, we study the number of intersections between $N (φ)$ and $γ$ in terms of $τ$ . When $Y$ is compact and $γ$ a geodesic circle, or when $Y$ has finite volume and $γ$ is a closed horocycle, we prove that $γ$ is “good” in the sense of [TZ]. As a result, we obtain that the number of intersections between $N (φ)$ and $γ$ is $O (τ)$ . This bound is sharp.

Sharp bounds for the number of the scattering poles

Georgi Vodev (1992)

Journées équations aux dérivées partielles

Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions of the laplacian on thin planar domains

Denis Borisov, Pedro Freitas (2009)

Annales de l'I.H.P. Analyse non linéaire

Small eigenvalues of Riemann surfaces and graphs.

Marc Burger (1990)

Mathematische Zeitschrift

Solutions to nonlinear elliptic equations with a nonlocal boundary condition.

Wang, Yuandi (2002)

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

Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

De Schepper, H. (1999)

Serdica Mathematical Journal

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads...

Some estimates concerning the Zeeman effect

Wiesław Cupała (1993)

Studia Mathematica

The Itô integral calculus and analysis on nilpotent Lie grops are used to estimate the number of eigenvalues of the Schrödinger operator for a quantum system with a polynomial magnetic vector potential. An analogue of the Cwikel-Lieb-Rosenblum inequality is proved.

Some Estimations of Positive and Negative Eigenvalues for an Inhomogeneous Membrane

Milutin Dostanić (1996)

Matematički Vesnik

Some logarithmic function spaces, entropy numbers, applications to spectral theory [Book]

Haroske Dorothee (1998)

Some new problems in spectral optimization

Giuseppe Buttazzo, Bozhidar Velichkov (2014)

Banach Center Publications

We present some new problems in spectral optimization. The first one consists in determining the best domain for the Dirichlet energy (or for the first eigenvalue) of the metric Laplacian, and we consider in particular Riemannian or Finsler manifolds, Carnot-Carathéodory spaces, Gaussian spaces. The second one deals with the optimal shape of a graph when the minimization cost is of spectral type. The third one is the optimization problem for a Schrödinger potential in suitable classes.

Currently displaying 1 – 20 of 42