Étude spectrale du système différentiel associé à un problème d’élasticité linéaire
Evolution by the vortex filament equation of curves with a corner
In this proceedings article we shall survey a series of results on the stability of self-similar solutions of the vortex filament equation. This equation is a geometric flow for curves in and it is used as a model for the evolution of a vortex filament in fluid mechanics. The main theorem give, under suitable assumptions, the existence and description of solutions generated by curves with a corner, for positive and negative times. Its companion theorem describes the evolution of perturbations...
Existence and multiplicity results for a semilinear elliptic eigenvalue problem
Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities
We study eigenvalue problems with discontinuous terms. In particular we consider two problems: a nonlinear problem and a semilinear problem for elliptic equations. In order to study the existence of solutions we replace these two problems with their multivalued approximations and, for the first problem, we estabilish an existence result while for the second problem we prove the existence of multiple nontrivial solutions. The approach used is variational.
Existence and perturbation of principal eigenvalues for a periodic-parabolic problem.
Existence and uniqueness for a -Laplacian nonlinear eigenvalue problem.
Existence des opérateurs d'ondes pour les systèmes hyperboliques avec un potentiel périodique en temps
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 positive solutions for two nonlinear eigenvalue problems.
Existence of Rayleigh resonances exponentially close to the real axis
Existence of solutions for an eigenvalue problem with weight.
Existence of solutions for some nonlinear elliptic equations.
Existence of three solutions to a double eigenvalue problem for the p-biharmonic equation
Using a three critical points theorem and variational methods, we study the existence of at least three weak solutions of the Navier problem ⎧ in Ω, ⎨ ⎩u = Δu = 0 on ∂Ω, where (N ≥ 1) is a non-empty bounded open set with a sufficiently smooth boundary ∂Ω, λ > 0, μ > 0 and f,g: Ω × ℝ → ℝ are two L¹-Carathéodory functions.
Existence results for quasilinear elliptic systems in .
Expansions and eigenfrequencies for damped wave equations
We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. In the strongly damped case, the propagator is shown to admit an expansion in terms of the finitely many eigenmodes near the real axis, with an error exponentially decaying in time. In the presence of an elliptic closed geodesic not meeting the support of the damping coefficient, we show that there exists a sequence of eigenfrequencies converging rapidly to the real axis. In the case of Zoll manifolds,...
Extension of analytic number theory and the theory of regularized harmonic series from Dirichlet series to Bessel series.
Extension of Díaz-Saá's inequality in RN and application to a system of p-Laplacian.
The purpose of this paper is to extend the Díaz-Saá’s inequality for the unbounded domains as RN.The proof is based on the Picone’s identity which is very useful in problems involving p-Laplacian. In a second part, we study some properties of the first eigenvalue for a system of p-Laplacian. We use Díaz-Saá’s inequality to prove uniqueness and Egorov’s theorem for the isolation. These results generalize J. Fleckinger, R. F. Manásevich, N. M. Stavrakakis and F. de Thélin’s work [9] for the first...
External finite element approximations of eigenvalue problems
Extrema de valeurs propres dans une classe conforme
On s’intéresse au problème de savoir quelle est la rigidité apportée au spectre d’une variété riemannienne compacte par le fait de fixer son volume et se classe conforme, et en particulier de déterminer si on peut faire tendre les valeurs propres vers 0 ou l’infini sous cette contrainte. On considère successivement les cas du laplacien usuel agissant sur les fonctions, l’opérateur de Dirac, le laplacien conforme et le laplacien de Hodge-de Rham.