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PreprintCC BY 4.0arXiv

Normalized ground states and a mass-constrained scattering threshold for the inhomogeneous NLS with an inverse-square potential

  • Mohamed Majdoub
  • Tarek Saanouni
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Abstract

We study the focusing inhomogeneous nonlinear Schrödinger equation with an inverse-square potential i∂t u+Δu−a|x|−2u+|x|−b|u|αu=0, (t,x)∈ℝ×ℝN, in the mass-supercritical and energy-subcritical regime (4−2b)/N<α<(4−2b)/(N−2), where N≥3 and 0<b<2. Two main lines of research have developed largely independently for this model: scattering theory below the ground-state threshold and the variational analysis of solutions with prescribed mass. In this work, we establish a connection between these two approaches.

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Cite

BibTeXRIS
BibTeX
@misc{majdoub2026normalized,
  title = {{Normalized ground states and a mass-constrained scattering threshold for the inhomogeneous NLS with an inverse-square potential}},
  author = {Mohamed Majdoub and Tarek Saanouni},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02933},
  eprint = {2610.02933},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02933},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Normalized ground states and a mass-constrained scattering threshold for the inhomogeneous NLS with an inverse-square potential
AU  - Mohamed Majdoub
AU  - Tarek Saanouni
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.02933
UR  - https://arxiv.org/abs/2610.02933
AB  - We study the focusing inhomogeneous nonlinear Schrödinger equation with an inverse-square potential i∂_t u+Δu−a|x|^−2u+|x|^−b|u|^αu=0, (t,x)∈ℝ×ℝ^N, in the mass-supercritical and energy-subcritical regime (4−2b)/N<α<(4−2b)/(N−2), where N≥3 and 0<b<2. Two main lines of research have developed largely independently for this model: scattering theory below the ground-state threshold and the variational analysis of solutions with prescribed mass. In this work, we establish a connection between these two approaches.
ER  -