Existence and perturbation of principal eigenvalues for a periodic-parabolic problem.
Existence of a principal eigenvalue for the Tricomi problem.
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 spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.
Existence of Rayleigh resonances exponentially close to the real axis
Existence of solutions for some nonlinear elliptic equations.
Finiteness of the Lower Spectrum of Schrödinger Operators.
Fonction spectrale d'opérateurs non elliptiques
Fonction zêta d'Epstein pour un opérateur elliptique qui dégénère dans la direction normale
Formule de Poisson pour les variétés riemanniennes.
Formule de trace et applications
Fredholm property for a parameter dependent second order operator differential equation.
Generalized Gaudin models and Riccatians
The systems of differential equations whose solutions exactly coincide with Bethe ansatz solutions for generalized Gaudin models are constructed. These equations are called the generalized spectral Riccati equations, because the simplest equation of this class has a standard Riccatian form. The general form of these equations is , i=1,..., r, where denote some homogeneous polynomials of degrees constructed from functional variables and their derivatives. It is assumed that . The problem...
Generic simplicity of eigenvalues for a Dirichlet problem of the bilaplacian operator.
Geometry of KDV (1): Addition and the unimodular spectral classes.
This is the first of three papers on the geometry of KDV. It presents what purports to be a foliation of an extensive function space into which all known invariant manifolds of KDV fit naturally as special leaves. The two main themes are addition (each leaf has its private one) and unimodal spectral classes (each leaf has a spectral interpretation).
Global Instability and Essential Spectrum in Semilinear Evolution Equations.
Hearing the shape of a compact Riemannian manifold with a finite number of piecewise impedance boundary conditions.
Hearing the shape of a general convex domain: an extension to higher dimensions
Homogenization of the criticality spectral equation in neutron transport
Homogenization of the criticality spectral equation in neutron transport
We address the homogenization of an eigenvalue problem for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclear reactor cores. We prove that the neutron flux, corresponding to the first and unique positive eigenvector, can be factorized in the product of two terms, up to a remainder which goes strongly to zero with the period. One term is the first eigenvector of the transport equation in the periodicity cell. The other term is the...
Hypoelliptic operators with characteristic variety of codimension two and the wave equation