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Stability of ground-states for a system of M coupled semilinear Schrödinger equations

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Abstract

We focus on the study of the stability properties of ground-states for the system of M coupled semilinear Schrödinger equations with power-type nonlinearities and couplings. Our results are generalizations of the theory for the single equation and the technique used is a simplification of the original one. Depending on the power of the nonlinearity, we may observe stability, instability and weak instability. We also obtain results for three distinct classes of bound-states, which is a special feature of the \({M \geqslant 2}\) case.

Mathematics Subject Classification

35Q55 35B35 35B40 

Keywords

Coupled semilinear Schrödinger equations Ground-states Stability 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.CMAF-UL and FCULLisboaPortugal

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