### Abstract

We consider a singular perturbation problem for a system of nonlinear Schrödinger equations:where N = 2, 3, μ_{1}, μ_{2}, β > 0 and V_{1}(x), V_{2}(x): R^{N} → (0, ∞) are positive continuous functions. We consider the case where the interaction β > 0 is relatively small and we define for P ε R^{N} the least energy level m(P) for non-trivial vector solutions of the rescaled "limit" problem: We assume that there exists an open bounded set Λ ⊂ R^{N} satisfying We show that (*) possesses a family of non-trivial vector positive solutions which concentrates-after extracting a subsequence e{open}_{n} → 0-to a point P_{0} ε Λ with m(P_{0}) = inf_{PεΛ}m(P). Moreover (v_{1e{open}}(x), v_{2e{open}}(x)) converges to a least energy non-trivial vector solution of (**) after a suitable rescaling.

Original language | English |
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Pages (from-to) | 449-480 |

Number of pages | 32 |

Journal | Calculus of Variations and Partial Differential Equations |

Volume | 40 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2011 Jan 1 |

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics