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Uniqueness and nondegeneracy of ground states for nonlinear Schrödinger equations with attractive inverse-power potential

This work was supported by Grant-in-Aid for JSPS Fellows 18J11090 and JSPS KAKENHI Grant Number 20K14349

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  • We study uniqueness and nondegeneracy of ground states for stationary nonlinear Schrödinger equations with a focusing power-type nonlinearity and an attractive inverse-power potential. We refine the results of Shioji and Watanabe (2016) and apply it to prove the uniqueness and nondegeneracy of ground states for our equations. We also discuss the orbital instability of ground state-standing waves.

    Mathematics Subject Classification: Primary: 35A02, 35Q55; Secondary: 35J61.

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