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

2019/03/25 by Fukaya, Noriyoshi · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.10227

Abstract

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.

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• Stability of standing waves for all frequencies to nonlinear Schrödinger equations with potentials in one dimension

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