A necessary condition for twin boundary layer behavior
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A note on eigenvalues of ordinary differential operators.
Alan Ho (1997)
Revista Matemática Iberoamericana
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
Manuel Núñez, Jesús Rojo (1993)
Applications of Mathematics
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.
Gorman, Arthur D. (1994)
International Journal of Mathematics and Mathematical Sciences
Almost Periodic Solutions of Singularly Perturbed Systems of Differential Equations with Impulse Effect.
Maria A. Hekimova, Drumi D. Bainov (1989)
Forum mathematicum
Asymptotic analysis of the Carrier-Pearson problem.
Lu, Chunqing (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Asymptotic expansions of canards with poles. Application to the stationary unidimensional Schrödinger equation.
Benoit, E. (1996)
Bulletin of the Belgian Mathematical Society - Simon Stevin
Asymptotique de solutions oscillantes d'équations différentielles
Franck Michel (1997)
Annales mathématiques Blaise Pascal
Boundary value problem with an inner point for the singularly perturbed semilinear differential equations
Róbert Vrábeľ (2011)
Mathematica Bohemica
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
Hans-Görg Roos (1979)
Commentationes Mathematicae Universitatis Carolinae
Eine Bemerkung zur WKB-Methode
Jiří Zeman (1978)
Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika
Estimations asymptotiques des intervalles d'instabilité pour l'équation de Hill
Alain Grigis (1987)
Annales scientifiques de l'École Normale Supérieure
Estimations asymptotiques des valeurs propres de l'équation de Hill polynomiale
Alain Grigis (1986)
Journées équations aux dérivées partielles
Existence and concentration of positive solutions for a quasilinear elliptic equation in .
Gloss, Elisandra (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
From multi-instantons to exact results
Jean Zinn-Justin (2003)
Annales de l’institut Fourier
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.
Zhou, Xiaobing, Jiang, Murong, Cai, Xiaomei (2011)
Discrete Dynamics in Nature and Society
Intervalles d'instabilité pour une équation de Hill à potentiel méromorphe
Thierry Ramond (1993)
Bulletin de la Société Mathématique de France
Introduction à la résurgence quantique
Frédéric Pham (1985/1986)
Séminaire Bourbaki
La variété des équations surstables
Guy Wallet (2000)
Bulletin de la Société Mathématique de France
Mathematical models for laser-plasma interaction
Rémi Sentis (2005)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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...
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