Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE ORBITAL STABILITY OF INHOMOGENEOUS NONLINEAR SCHRÖDINGER EQUATIONS WITH SINGULAR POTENTIAL

  • Cho, Yonggeun (Department of Mathematics and Institute of Pure and Applied Mathematics Chonbuk National University) ;
  • Lee, Misung (Department of Mathematics Chonbuk National University)
  • Received : 2019.01.08
  • Accepted : 2019.04.12
  • Published : 2019.11.30
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Abstract

We show the existence of ground state and orbital stability of standing waves of nonlinear $Schr{\ddot{o}}dinger$ equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in $H^1$. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in [5, 12] slightly in 3 dimensions.

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References

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