Louis Dupaigne
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Louis Dupaigne has a total of 32 co-authors. Here are the top co-authors by number of shared publications:
- Alberto Farina
LAMFA, UMR CNRS 7352, Université Picardie Jules Verne, Amiens, France
7 shared publications - Marius Ghergu
School of Mathematics and Statistics, University College Dublin, Dublin, Ireland
7 shared publications - Olivier Goubet
Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, CNRS UMR 7352, Université de Picardie Jules Verne, 80039 Amiens, France
6 shared publications - Juan Dávila
Department of Mathematical Sciences, University of Bath, Bath, UK
5 shared publications - Marcelo Montenegro
Universidade Estadual de Campinas
4 shared publications - Guillaume Warnault
LMAP, UMR E2S UPPA CNRS 5142, Université de Pau et Pays de l’Adour, Pau, France
3 shared publications
Latest Publications
- 28 March 2025
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 64 (4) , 1-26
Asymptotically homogeneous solutions of the supercritical Lane-Emden system
- 28 March 2025
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 64 (4) , 1-26
Asymptotically homogeneous solutions of the supercritical Lane-Emden system
- Open Access
Asymptotically homogeneous solutions of the supercritical Lane-Emden system
We consider the Lane-Emden system-$Δ$u = |v| p-1 v,-$Δ$v = |u| q-1 u in R d. When p $\ge$ q $\ge$ 1, it is known that there exists a positive radial stable solution (u, v) $\in$ C 2 (R d) if and only if d $\ge$ 11 and (p, q) lies on or above the so-called Joseph-Lundgren curve introduced in [5]. In this paper, we prove that for d $\le$ 10, there is no positive stable solution (or merely stable outside a compact set and (p, q) does not lie on the critical Sobolev hyperbola), while for d $\ge$ 11, the Joseph-Lundgren curve is indeed the dividing line for the existence of such solutions, if one assumes in addition that they are asymptotically homogeneous (see Definition 1 below). Most of our results are optimal improvements of previous works in the litterature.Open AccessAsymptotically homogeneous solutions of the supercritical Lane-Emden system
We consider the Lane-Emden system-$Δ$u = |v| p-1 v,-$Δ$v = |u| q-1 u in R d. When p $\ge$ q $\ge$ 1, it is known that there exists a positive radial stable solution (u, v) $\in$ C 2 (R d) if and only if d $\ge$ 11 and (p, q) lies on or above the so-called Joseph-Lundgren curve introduced in [5]. In this paper, we prove that for d $\le$ 10, there is no positive stable solution (or merely stable outside a compact set and (p, q) does not lie on the critical Sobolev hyperbola), while for d $\ge$ 11, the Joseph-Lundgren curve is indeed the dividing line for the existence of such solutions, if one assumes in addition that they are asymptotically homogeneous (see Definition 1 below). Most of our results are optimal improvements of previous works in the litterature. - 23 February 2023
- Published by Elsevier in Journal of Functional Analysis
- Vol. 284 (10)
Liouville-type theorems for the Lane-Emden equation in the half-space and cones
- 23 February 2023
- Published by Elsevier in Journal of Functional Analysis
- Vol. 284 (10)
Liouville-type theorems for the Lane-Emden equation in the half-space and cones
- Open Access
Liouville-type theorems for the Lane-Emden equation in the half-space and cones
We prove that 0 the only classical solution of the Lane-Emden equation in the half-space which is stable outside a compact set. We also consider weak solutions and the case of general cones.
Open AccessLiouville-type theorems for the Lane-Emden equation in the half-space and cones
We prove that 0 the only classical solution of the Lane-Emden equation in the half-space which is stable outside a compact set. We also consider weak solutions and the case of general cones.
- Open Access
- 12 April 2022
- Published by Mathematical Sciences Publishers in Analysis & PDE
- Vol. 15 (2) , 551-566
Classification and Liouville-type theorems for semilinear elliptic equations in unbounded domains
- 12 April 2022
- Published by Mathematical Sciences Publishers in Analysis & PDE
- Vol. 15 (2) , 551-566
Open AccessClassification and Liouville-type theorems for semilinear elliptic equations in unbounded domains
- Open Access
A Liouville-type theorem for the Lane-Emden equation in a half-space
We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solution which is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution which is bounded on finite strips. This question has a long history and our result solves a long-standing open problem. Such a nonexistence result was previously available only for bounded solutions, or under a restriction on the power in the nonlinearity. The result extends to general convex nonlinearities.
Open AccessA Liouville-type theorem for the Lane-Emden equation in a half-space
We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solution which is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution which is bounded on finite strips. This question has a long history and our result solves a long-standing open problem. Such a nonexistence result was previously available only for bounded solutions, or under a restriction on the power in the nonlinearity. The result extends to general convex nonlinearities.
- Open Access
Classification and Liouville-type theorems for semilinear elliptic equations in unbounded domains
We classify stable and finite Morse index solutions to general semilinear elliptic equations posed in Euclidean space of dimension at most 10, or in some unbounded domains.
Open AccessClassification and Liouville-type theorems for semilinear elliptic equations in unbounded domains
We classify stable and finite Morse index solutions to general semilinear elliptic equations posed in Euclidean space of dimension at most 10, or in some unbounded domains.
- Open Access
- 20 November 2017
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 148 (1) , 51-62
The Lane–Emden equation in strips
We study the Lane–Emden equation in strips.
- 20 November 2017
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 148 (1) , 51-62
Open AccessThe Lane–Emden equation in strips
We study the Lane–Emden equation in strips.
- Open Access
- 16 May 2017
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 369 (9) , 6087-6104
On the fractional Lane-Emden equation
We classify solutions of finite Morse index of the fractional Lane-Emden equation \[ \]- 16 May 2017
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 369 (9) , 6087-6104
Open AccessOn the fractional Lane-Emden equation
We classify solutions of finite Morse index of the fractional Lane-Emden equation \[ \] - Open Access
On the fractional Lane-Emden equation
We classify solutions of finite Morse index of the fractional Lane- Emden equation
Open AccessOn the fractional Lane-Emden equation
We classify solutions of finite Morse index of the fractional Lane- Emden equation