A necessary condition for twin boundary layer behavior
A note on eigenvalues of ordinary differential operators.
In this follow-up on the work of Fefferman-Seco [FS] an improved condition for the discrete eigenvalues of the operator -d2 / dx2 + V(x) is established for V(x) satisfying certain hypotheses. The eigenvalue condition in [FS] establishes eigenvalues of this operator to within a small error. Through an obervation due to C. Fefferman, the order of accuracy can be improved if a certain condition is true. This paper improves on the result obtained in [FS] by showing that this condition does indeed hold....
A WKB analysis of the Alfvén spectrum of the linearized magnetohydrodynamics equations
Small perturbations of an equilibrium plasma satisfy the linearized magnetohydrodynamics equations. These form a mixed elliptic-hyperbolic system that in a straight-field geometry and for a fixed time frequency may be reduced to a single scalar equation div, where may have singularities in the domaind of definition. We study the case when is a half-plane and possesses high Fourier components, analyzing the changes brought about by the singularity . We show that absorptions of energy takes...
Addendum to a paper of Craig and Goodman.
Almost Periodic Solutions of Singularly Perturbed Systems of Differential Equations with Impulse Effect.
Asymptotic analysis of the Carrier-Pearson problem.
Asymptotic expansions of canards with poles. Application to the stationary unidimensional Schrödinger equation.
Asymptotique de solutions oscillantes d'équations différentielles
Boundary value problem with an inner point for the singularly perturbed semilinear differential equations
In this paper we investigate the problem of existence and asymptotic behavior of solutions for the nonlinear boundary value problem satisfying three point boundary conditions. Our analysis relies on the method of lower and upper solutions and delicate estimations.
Die Konstruktion asymptotischer Fundamentalsysteme für lineare Differentialgleichungen mit Wendepunkten
Eine Bemerkung zur WKB-Methode
Estimations asymptotiques des intervalles d'instabilité pour l'équation de Hill
Estimations asymptotiques des valeurs propres de l'équation de Hill polynomiale
Existence and concentration of positive solutions for a quasilinear elliptic equation in .
From multi-instantons to exact results
In these notes, conjectures about the exact semi-classical expansion of eigenvalues of hamiltonians corresponding to potentials with degenerate minima, are recalled. They were initially motivated by semi-classical calculations of quantum partition functions using a path integral representation and have later been proven to a large extent, using the theory of resurgent functions. They take the form of generalized Bohr--Sommerfeld quantization formulae. We explain here their...
Hopf bifurcation analysis for the van der Pol equation with discrete and distributed delays.
Intervalles d'instabilité pour une équation de Hill à potentiel méromorphe
Introduction à la résurgence quantique
La variété des équations surstables
Mathematical models for laser-plasma interaction
We address here mathematical models related to the Laser-Plasma Interaction. After a simplified introduction to the physical background concerning the modelling of the laser propagation and its interaction with a plasma, we recall some classical results about the geometrical optics in plasmas. Then we deal with the well known paraxial approximation of the solution of the Maxwell equation; we state a coupling model between the plasma hydrodynamics and the laser propagation. Lastly, we consider the...