In this paper we focus on existence and symmetry properties of solutions to the cubic Schrödinger system -δui + λiui = ∑j=1d βijuj2ui in Ω ⊂ RN, i = 1, . . . d where d ≥ 2, λi, βii > 0, βij = βji ∈ R for j ≠ i, N = 2, 3. The underlying domain Ω is either bounded or the whole space, and ui ∈ H01(Ω) or ui ∈ Hrad1(RN) respectively. We establish new existence and symmetry results for least energy positive solutions in the case of mixed cooperation and competition coefficients, as well as in the purely cooperative case.

New existence and symmetry results for least energy positive solutions of Schrödinger systems with mixed competition and cooperation terms

SOAVE, NICOLA;
2016

Abstract

In this paper we focus on existence and symmetry properties of solutions to the cubic Schrödinger system -δui + λiui = ∑j=1d βijuj2ui in Ω ⊂ RN, i = 1, . . . d where d ≥ 2, λi, βii > 0, βij = βji ∈ R for j ≠ i, N = 2, 3. The underlying domain Ω is either bounded or the whole space, and ui ∈ H01(Ω) or ui ∈ Hrad1(RN) respectively. We establish new existence and symmetry results for least energy positive solutions in the case of mixed cooperation and competition coefficients, as well as in the purely cooperative case.
Competitive and cooperative systems; Foliated Schwarz symmetry; Least energy positive solutions; Nehari manifold; Positive solutions; Schrödinger cubic systems; Analysis
File in questo prodotto:
File Dimensione Formato  
11311-1007044_Soave.pdf

accesso aperto

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 579.58 kB
Formato Adobe PDF
579.58 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1007044
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 33
  • ???jsp.display-item.citation.isi??? 32
social impact