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

Autor(es)

Bonheure, Denis ^[1] ; dos Santos, Ederson Moreira ^[2] ; Ramos, Miguel ^[3] ; Tavares, Hugo ^[4]

Afiliação do(s) autor(es)

^[1] Univ Libre Bruxelles, Dept Math, B-1050 Brussels - Belgium

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

^[3] Univ Lisbon, Fac Sci, CMAF, P-1649003 Lisbon - Portugal

^[4] Univ Lisbon, Inst Super Tecn, Ctr Math Anal Geometry & Dynam Syst, Dept Math, P-1049001 Lisbon - Portugal

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES; v. 104, n. 6, p. 1075-1107, DEC 2015.
• Citações Web of Science: 5

Resumo

In this paper we prove existence of least energy nodal solutions for the Hamiltonian elliptic system with Henon-type weights -Delta u = vertical bar x vertical bar(beta)vertical bar v vertical bar(q-1)v, -Delta u = vertical bar x vertical bar(alpha)vertical bar u vertical bar(q-1)u in Omega, u = v = 0 on partial derivative Omega where Omega is a bounded smooth domain in R-N, N >= 1, alpha, beta >= 0 and the nonlinearities are superlinear and subcritical, namely 1 > 1/p+1 + 1/q+1 > N - 2/N. When Omega is either a ball or an annulus centred 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. (C) 2015 Elsevier Masson SAS. All rights reserved. (AU)

• Processo FAPESP: 14/03805-2 - Equações e sistemas de equações diferenciais parciais elípticas não lineares
• Beneficiário: Ederson Moreira dos Santos
• Modalidade de apoio: Bolsas no Exterior - Pesquisa