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
