Bound states for a coupled Schrödinger system

@inproceedings{Bartsch2007BoundSF,
  title={Bound states for a coupled Schr{\"o}dinger system},
  author={Thomas Bartsch and Zhi-qiang Wang and Juncheng Wei},
  year={2007}
}
We consider the existence of bound states for the following coupled elliptic system ∆u1 − λ1u1 + μ1u1 + βu2u1 = 0 in R, ∆u2 − λ2u2 + μ2u2 + βu1u2 = 0 in R, u1 > 0, u2 > 0, u1, u2 ∈ H(R) where n ≤ 3. Using the fixed point index in cones we prove the existence of a five-dimensional continuum C ⊂ R+ × H(R) × H(R) of solutions (λ1, λ2, μ1, μ2, β, u1, u2) bifurcating from the set of semipositive solutions (where u1 = 0 or u2 = 0) and investigate the parameter range covered by C. 
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