Existence and symmetry of least energy nodal solutions for Hamiltonian elliptic systems

Bonheure, Denis; Moreira dos Santos, Ederson; Ramos, Miguel; Tavares, Hugo

Type de document :

Article dans une revue scientifique: Article original

DOI :

10.1016/j.matpur.2015.07.005

Titre :

Existence and symmetry of least energy nodal solutions for Hamiltonian elliptic systems

Auteur(s) :

Bonheure, Denis [Auteur]
Quantitative methods for stochastic models in physics [MEPHYSTO]
Département de mathématiques Université Libre de Bruxelles
Moreira dos Santos, Ederson [Auteur]
Instituto de Ciências Mathemàticas e de Computação [São Carlos] [ICMC-USP]
Ramos, Miguel [Auteur]
Universidade de Lisboa = University of Lisbon = Université de Lisbonne [ULISBOA]
Tavares, Hugo [Auteur]
Instituto Superior Técnico [IST / Técnico Lisboa]

Titre de la revue :

Journal de Mathématiques Pures et Appliquées

Pagination :

doi:10.1016/j.matpur.2015.07.005

Éditeur :

Elsevier

Date de publication :

2015

ISSN :

0021-7824

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

Résumé en anglais : [en]

In this paper we prove existence of least energy nodal solutions for the Hamiltonian elliptic system with Hénon –type weights −∆u = |x| β |v| q−1 v, −∆v = |x| α |u| p−1 u in Ω, u = v = 0 on ∂Ω, where Ω is a bounded smooth ...
Lire la suite >In this paper we prove existence of least energy nodal solutions for the Hamiltonian elliptic system with Hénon –type weights −∆u = |x| β |v| q−1 v, −∆v = |x| α |u| p−1 u in Ω, u = v = 0 on ∂Ω, where Ω is a bounded smooth domain in R N , N ≥ 1, α, β ≥ 0 and the nonlinearities are superlinear and subcritical, namely 1 > 1 p + 1 + 1 q + 1 > N − 2 N. When Ω is either a ball or an annulus centered at the origin and N ≥ 2, we show that these solutions display the so-called foliated Schwarz symmetry. It is natural to conjecture that these solutions are not radially symmetric. We provide such a symmetry breaking in a range of parameters where the solutions of the system behave like the solutions of a single equation. Our results on the above system are new even in the case of the Lane-Emden system (i.e. without weights). As far as we know, this is the first paper that contains results about least energy nodal solutions for strongly coupled elliptic systems and their symmetry properties.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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