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Existence and concentration of ground states of coupled nonlinear Schrödinger equations with bounded potentials

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Abstract

A 2-coupled nonlinear Schrödinger equations with bounded varying potentials and strongly attractive interactions is considered. When the attractive interaction is strong enough, the existence of a ground state for sufficiently small Planck constant is proved. As the Planck constant approaches zero, it is proved that one of the components concentrates at a minimum point of the ground state energy function which is defined in Section 4.

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Authors and Affiliations

  1. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Gongming Wei

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  1. Gongming Wei
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Correspondence to Gongming Wei.

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Project supported by the Research Project of Shanghai Municipal Education Commission (No. 07zz83).

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Wei, G. Existence and concentration of ground states of coupled nonlinear Schrödinger equations with bounded potentials. Chin. Ann. Math. Ser. B 29, 247–264 (2008). https://doi.org/10.1007/s11401-007-0104-4

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  • DOI: https://doi.org/10.1007/s11401-007-0104-4

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