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.
Extremal properties of the first eigenvalue of a class of elliptic eigenvalue problems
Extremal values of half-eigenvalues for -Laplacian with weights in balls.
Ferromagnetic integrals, correlations and maximum principles
For correlations of the form (0.2) we consider a critical case and prove power decay upper bounds in terms of the fundamental solution of a certain elliptic operator. This is achieved by improving the use of a maximum principle. We also formulate a general maximum principle and give two applications.
Finite Dimensional Approximation of Bifurcation Problems in Presence of Symmetries.
Finite eigenfunction approximations for continuous spectrum operators.
Finite element approximation of a non-Lipschitz nonlinear eigenvalue problem
Finite element approximation of the first eigenvalue of a nonlinear problem for some special domains.
Finiteness of the Lower Spectrum of Schrödinger Operators.
Focusing of a pulse with arbitrary phase shift for a nonlinear wave equation
We consider a system of two linear conservative wave equations, with a nonlinear coupling, in space dimension three. Spherical pulse like initial data cause focusing at the origin in the limit of short wavelength. Because the equations are conservative, the caustic crossing is not trivial, and we analyze it for particular initial data. It turns out that the phase shift between the incoming wave (before the focus) and the outgoing wave (past the focus) behaves like , where stands for the wavelength....