UNIQUENESS and NONDEGENERACY of GROUND STATES for NONLINEAR SCHRÖDINGER EQUATIONS with ATTRACTIVE INVERSE-POWER POTENTIAL

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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.

Original languageEnglish
Pages (from-to)121-143
Number of pages23
JournalCommunications on Pure and Applied Analysis
Volume20
Issue number1
DOIs
Publication statusPublished - Jan 2021

Keywords

  • And phrases. Uniqueness
  • Ground state
  • Instability
  • Inverse-power potential
  • Nondegeneracy
  • Nonlinear Schrödinger equation
  • Standing wave

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