Eine Bemerkung zur lokalen Werteverteilung der Lösungen linearer Differentialgleichungen.
Eine Verallgemeinerte Fuchs'sche Theorie.
Elementary Acceleration and Multisummability I
Elementary acceleration and multisummability. I
Elementary Solution of Vecua Equation With Analytic Coefficients on Z,
Équation de Hill à potentiel méromorphe
Equation coefficient of which has a small modulus
Équations différentielles à points singuliers irréguliers en dimension 2
Erweiterung des Abel'schen Satzes von der Form der algebraisch-logarithmisch ausdrückbaren Integrale algebraischer Functionen
Essential singular points of solutions of an algebraic differential equation.
Estimation of the hyper-order of entire solutions of complex linear ordinary differential equations whose coefficients are entire functions.
Étude des solutions surstables de l'équation de Van der Pol
Euler's integral transformation for systems of linear differential equations with irregular singularities
Dettweiler and Reiter formulated Euler's integral transformation for Fuchsian systems of differential equations and applied it to a definition of the middle convolution. In this paper, we formulate Euler's integral transformation for systems of linear differential equations with irregular singularities. We show by an example that the confluence of singularities is compatible with Euler's integral transformation.
Exceptional Values of Solutions of Linear Differential Equations.
Exemples de hamiltoniens non intégrables en mécanique analytique réelle
Existence and uniqueness of analytic solutions of the Shabat equation.
Existence of meromorphic solutions of algebraic differential equations.
Explicit rational solutions of Knizhnik-Zamolodchikov equation
We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions generated by elements of the symmetric group n. We assume that parameter ρ = ±1. In previous paper [5] we proved that the fundamental solution of the corresponding KZ-equation is rational. Now we construct this solution in the explicit form.
Factorisation d'opérateurs différentiels à coefficients dans une extension liouvillienne d'un corps valué
On démontre ici un lemme de Hensel pour les opérateurs différentiels. On en déduit un théorème de factorisation pour des opérateurs différentiels à coefficients dans une extension liouvillienne transcendante d’un corps valué. On obtient en particulier un théorème de factorisation pour des opérateurs différentiels à coefficients dans une extension de par un nombre fini d’exponentielles et de logarithmes algébriquement indépendants sur .
Families of linear differential equations related to the second Painlevé equation
This paper is a sequel to [vdP-Sa] and [vdP]. The two classes of differential modules (0,-,3/2) and (-,-,3), related to PII, are interpreted as fine moduli spaces. It is shown that these moduli spaces coincide with the Okamoto-Painlevé spaces for the given parameters. The geometry of the moduli spaces leads to a proof of the Painlevé property for PII in standard form and in the Flaschka-Newell form. The Bäcklund transformations, the rational solutions and the Riccati solutions for PII are derived...