Existence and bounds for nonlinear Schrödinger systems with strong competition

Article type: Research Article

Authors: Domingos, Ana Rute | Ramos, Miguel^;

Affiliations: CMAF – Faculty of Science, University of Lisbon, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal. Tel.: +351 217 904 911; Fax: +351 217 954 288; E-mails: {rute, mramos}@ptmat.fc.ul.pt

Note: [] Corresponding author. E-mail: [email protected].

Abstract: We consider systems of coupled Schrödinger equations which appear in nonlinear optics and binary Bose–Einstein condensation. Namely, we prove that for most μ,ν∈R, a,b>0, the system −Δu=μu+au3−βuv2, −Δv=νv+bv3−βvu2, u,v∈H10(B1(0)), where B1(0) is the unit ball of R3, admits a family of radially symmetric positive solutions (uβ,vβ) provided the interaction parameter β>0 is sufficiently large. By using a Morse index technique we deduce that these solutions are bounded uniformly in β, hence their limit functions as β→∞ undergo the phenomenon of phase segregation.

Keywords: elliptic systems, phase segregation, Fučík spectrum, linking, Morse index

DOI: 10.3233/ASY-2012-1097

Journal: Asymptotic Analysis, vol. 80, no. 1-2, pp. 1-19, 2012