36 pages. Following the referee's comments, we have clarified the exposition of some proofs and corrected some misprintsInternational audienceThis paper is divided in two parts. In the first part we consider irregular singular analytic q-difference equations, with q\in ]0,1[, and we show how the Borel sum of a divergent solution of a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of such a q-difference equation. In the second part, we work under the assumption q\in ]1,+\infty[. In this case, at least four different q-Borel sums of a divergent solution of an irregular singular analytic q-difference equations are spread in the literature: under convenient assumptions we clarify the relatio...
AbstractUnder a certain restriction, singular first-order linear partial differential equations of n...
Consider a linear $ q $-difference equation: $ a(z)f(z) = b(z)f(qz) + c(z) $, $ 0 < mid q mid < 1 $,...
In this paper, we study q-difference analogues of several central results in value distribution theo...
International audienceIn this paper, we consider a q-analogue of the Borel-Laplace summation where q...
In this article, we construct explicit meromorphic solutions of first order linear q-difference equa...
Ce papier a été initialement écrit sous le titre suivant : "Computing Bugeaud's solutions of q-diffe...
The aim of this work is to establish the existence, uniqueness and q-Gevrey character of formal powe...
Let q > 1. The paper considers a linear q-difference-differential equation: it is a q-difference equ...
AbstractWe investigate the growth of transcendental meromorphic solutions of some complex q-differen...
This paper is concerned with the study of the Borel summability of divergent solutions for singularl...
The content of this paper was previously included in arXiv:1002.4839International audienceWe establi...
AbstractThis article part I and the forthcoming part II are concerned with the study of the Borel su...
Borel summable divergent series usually appear when studying solutions of analytic ODE near a multip...
A family of linear singularly perturbed difference differential equations is examined. These equatio...
This thesis deal with the differential Galois theory and more particularly the Borel-Laplace summati...
AbstractUnder a certain restriction, singular first-order linear partial differential equations of n...
Consider a linear $ q $-difference equation: $ a(z)f(z) = b(z)f(qz) + c(z) $, $ 0 < mid q mid < 1 $,...
In this paper, we study q-difference analogues of several central results in value distribution theo...
International audienceIn this paper, we consider a q-analogue of the Borel-Laplace summation where q...
In this article, we construct explicit meromorphic solutions of first order linear q-difference equa...
Ce papier a été initialement écrit sous le titre suivant : "Computing Bugeaud's solutions of q-diffe...
The aim of this work is to establish the existence, uniqueness and q-Gevrey character of formal powe...
Let q > 1. The paper considers a linear q-difference-differential equation: it is a q-difference equ...
AbstractWe investigate the growth of transcendental meromorphic solutions of some complex q-differen...
This paper is concerned with the study of the Borel summability of divergent solutions for singularl...
The content of this paper was previously included in arXiv:1002.4839International audienceWe establi...
AbstractThis article part I and the forthcoming part II are concerned with the study of the Borel su...
Borel summable divergent series usually appear when studying solutions of analytic ODE near a multip...
A family of linear singularly perturbed difference differential equations is examined. These equatio...
This thesis deal with the differential Galois theory and more particularly the Borel-Laplace summati...
AbstractUnder a certain restriction, singular first-order linear partial differential equations of n...
Consider a linear $ q $-difference equation: $ a(z)f(z) = b(z)f(qz) + c(z) $, $ 0 < mid q mid < 1 $,...
In this paper, we study q-difference analogues of several central results in value distribution theo...