On the essential spectrum of many-particle pseudorelativistic Hamiltonians with permutational symmetry account.
On the existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems.
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 existence of positive solutions for periodic parabolic sublinear problems.
On the generic spectrum of a riemannian cover
Let be a compact manifold let be a finite group acting freely on , and let be the (Fréchet) space of -invariant metric on . A natural conjecture is that, for a generic metric in , all eigenspaces of the Laplacian are irreducible (as orthogonal representations of ). In physics terminology, no “accidental degeneracies” occur generically. We will prove this conjecture when dim dim for all irreducibles of . As an application, we construct isospectral manifolds with simple eigenvalue...
On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundary
In this paper we study the behavior of solutions of the boundary value problem for the Poisson equation in a partially perforated domain with arbitrary density of cavities and mixed type conditions on their boundary. The corresponding spectral problem is also considered. A short communication of similar results can be found in [1].
On the linearization of some singular, nonlinear elliptic problems and applications
On the nodal line of the second eigenfunction of elliptic operators in two dimensions.
On the nodal set of the second eigenfunction of the laplacian in symmetric domains in
We present a simple proof of the fact that if is a bounded domain in , , which is convex and symmetric with respect to orthogonal directions, , then the nodal sets of the eigenfunctions of the laplacian corresponding to the eigenvalues must intersect the boundary. This result was proved by Payne in the case for the second eigenfunction, and by other authors in the case of convex domains in the plane, again for the second eigenfunction.
On the point spectrum of Schrödinger operators
On the scattering theory of the Laplacian with a periodic boundary condition. II. Additional channels of scattering.
On the scattering theory of the Laplacian with a periodic boundary condition. I. Existence of wave operators.
On the singular set, the resolvent and Fermi's Golden Rule for finite volume hyperbolic surfaces.
On the spectcral theory of elliptic differential operators. I.
On the Spectra of Schrödinger Operators with a Complex Potential.
On the spectral geometry of algebraic curves.
On the spectral theory of pseudo-differential elliptic boundary problems
On the spectrum and eigenfunctions of the Schrödinger operator with Aharonov–Bohm magnetic field.
On the spectrum of a nonlinear planar problem
On the spectrum of the reduced wave operators with cylindrical discontinuity.
On the structure of the spectrum for the elasticity problem in a body with a supersharp spike.