Sobre La Cohomologia Asociada A Un Operador Lineal Diferencial Complejo.
Solution of the Schwarz differential equation.
Solutions entières d'un système d'équations aux différences. II
Soit un entier naturel non nul, et une fonction entière de variables complexes. Dans un article précédent, nous avons démontré dans le cas , que si est une solution d’un système de équations aux différences à coefficients polynomiaux dans deux directions différentes, avec une condition restrictive portant sur les équations, alors est le quotient d’un polynôme exponentiel par un polynôme. Dans cet article, nous démontrons ce résultat dans le cas général, et l’analogue pour le cas de...
Solutions of with prescribed sequences of zeros.
Solutions of that have almost all real zeros.
Solutions of non-homogeneous linear differential equations in the unit disc
The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation , where all coefficients , F ≢ 0 are analytic functions in the unit disc = z∈ℂ: |z|<1. We obtain some results classifying the growth of finite iterated order solutions in terms of the coefficients with finite iterated type. The convergence exponents of zeros and fixed points of solutions are also investigated.
Solutions of nonhomogeneous linear differential equations with exceptionally few zeros.
Solutions surstables des équations différentielles complexes lentes-rapides à point tournant
Solving higher order Fuchs type differential systems avoiding the increase of the problem dimension.
Some addition to the generalized Riemann-Hilbert problem
We consider the generalized Riemann-Hilbert problem for linear differential equations with irregular singularities. If one weakens the conditions by allowing one of the Poincaré ranks to be non-minimal, the problem is known to have a solution. In this article we give a bound for the possibly non-minimal Poincaré rank. We also give a bound for the number of apparent singularities of a scalar equation with prescribed generalized monodromy data.
Some examples for the Poincaré and Painlevé problems
Some Examples of Rigid Representations
*Research partially supported by INTAS grant 97-1644.Consider the Deligne-Simpson problem: give necessary and sufficient conditions for the choice of the conjugacy classes Cj ⊂ GL(n,C) (resp. cj ⊂ gl(n,C)) so that there exist irreducible (p+1)-tuples of matrices Mj ∈ Cj (resp. Aj ∈ cj) satisfying the equality M1 . . .Mp+1 = I (resp. A1+. . .+Ap+1 = 0). The matrices Mj and Aj are interpreted as monodromy operators and as matrices-residua of fuchsian systems on Riemann’s sphere. We give new examples...
Some precise estimates of the hyper order of solutions of some complex linear differential equations.
Some Results on Hypertranscendental Meromorphic Functions.
Some results on the complex oscillation theory of differential equations with polynomial coefficients.
Some results on the complex oscillation theory of some differential polynomials.
Some Results on the Properties of Differential Polynomials Generated by Solutionsof Complex Differential Equations
This paper is devoted to considering the complex oscillation of differential polynomials generated by meromorphic solutions of the differential equation where
Sommation effective d’une somme de Borel par séries de factorielles
Nous abordons dans cet article la question de la sommation effective d’une somme de Borel d’une série par la série de factorielles associée. Notre approche fournit un contrôle de l’erreur entre la somme de Borel recherchée et les sommes partielles de la série de factorielles. Nous généralisons ensuite cette méthode au cadre des séries de puissances fractionnaires, après avoir démontré un analogue d’un théorème de Nevanlinna de sommation de Borel fine pour ce cadre.
Stokes matrices of hypergeometric integrals
In this work we compute the Stokes matrices of the ordinary differential equation satisfied by the hypergeometric integrals associated to an arrangement of hyperplanes in generic position. This generalizes the computation done by J.-P. Ramis for confluent hypergeometric functions, which correspond to the arrangement of two points on the line. The proof is based on an explicit description of a base of canonical solutions as integrals on the cones of the arrangement, and combinatorial relations between...
Stokes multipliers for subdominant solutions of second order differential equations with polynomial coefficients.