592 citations
- Université de LimogesFR138 papers
- Centre National de la Recherche ScientifiqueFR112 papers
- University of BresciaIT14 papers
- Institut national de recherche en sciences et technologies du numériqueFR11 papers
- Sorbonne UniversitéFR11 papers
- Université de PoitiersFR11 papers
- Laboratoire Interdisciplinaire Carnot de BourgogneFR9 papers
- Sapienza University of RomeIT9 papers
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8 papers · 1 filter
Darboux Transformations for Orthogonal Differential Systems and Differential Galois Theory
Primitivo Acosta-Humánez, Moulay Barkatou, Raquel Sánchez-Cauce +1
Darboux developed an ingenious algebraic mechanism to construct infinite chains of ''integrable'' second-order differential equations as well as their solutions. After a surprising…
Linear Differential Systems with Small Coefficients: Various Types of Solvability and their Verification
Moulay A. Barkatou, Renat R. Gontsov
We study the problem of solvability of linear differential systems with small coefficients in the Liouvillian sense (or, by generalized quadratures). For a general system, this pro…
Ekeland's inverse function theorem in graded Fréchet spaces revisited for multifunctions
Van Ngai Huynh, Michel Théra
In this paper, we present some implicit function theorems for set-valued mappings between Fréchet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekelan…
Liouville integrability: an effective Morales-Ramis-Simó theorem
Ainhoa Aparicio-Monforte, Thomas Dreyfus, Jacques-Arthur Weil
Consider a complex Hamiltonian system and an integral curve. In this paper, we give an effective and efficient procedure to put the variational equation of any order along the inte…
Galoisian Methods for Testing Irreducibility of Order Two Nonlinear Differential Equations
Guy Casale, Jacques-Arthur Weil
The aim of this article is to provide a method to prove the irreducibility of non-linear ordinary differential equations by means of the differential Galois group of their variatio…
Differential Galois Theory and Lie Symmetries
David Blázquez-Sanz, Juan J. Morales-Ruiz, Jacques-Arthur Weil
We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetri…