Note on the multiplicity of solutions for nonlinear scalar field equations with a critical inverse-square potential

Bartosz Bieganowski; Daniel Strzelecki

Note on the multiplicity of solutions for nonlinear scalar field equations with a critical inverse-square potential

Analysis of PDEs 2026-01-22 v1

Authors: Bartosz Bieganowski , Daniel Strzelecki

Abstract

We are interested in the multiplicity of solutions to the following scalar field equation $-\Delta u - \frac{(N-2)^2}{4|x|^2} u = g(u), \quad \mbox{in } \mathbb{R}^N \setminus \{0\}.$ We establish the existence of infinitely many radial and non-radial solutions.

Keywords

nonlinear scalar field equation inverse-square potential multiplicity of solutions radial solutions critical potential

Cite

@article{arxiv.2601.15003,
  title  = {Note on the multiplicity of solutions for nonlinear scalar field equations with a critical inverse-square potential},
  author = {Bartosz Bieganowski and Daniel Strzelecki},
  journal= {arXiv preprint arXiv:2601.15003},
  year   = {2026}
}

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