Uniqueness of ground states of some coupled nonlinear Schrodinger systems and their application

Details Uniqueness of ground states of some coupled nonlinear Schrodinger systems and their application Uniqueness of ground states of some coupled nonlinear Schrodinger systems and their application

2007-08-02

arxiv.org/abs/0708.0284v1

Mathematics

Analysis of PDEs

14 pages

Scientific paper

We establish the uniqueness of ground states of some coupled nonlinear Schrodinger systems in the whole space. We firstly use Schwartz symmetrization to obtain the existence of ground states for a more general case. To prove the uniqueness of ground states, we use the radial symmetry of the ground states to transform the systems into an ordinary differential system, and then we use the integral forms of the system. More interestingly, as an application of our uniqueness results, we derive a sharp vector-valued Gagliardo-Nirenberg inequality.

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