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May 27, 2026Analysis and Mathematical Physics0 citationsOpen Access

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

BBBartosz BieganowskiDSDaniel Strzelecki

Key Points

  • This note investigates the existence of multiple solutions to a specific scalar field equation with a critical potential.
  • Analyzed the scalar field equation involving the Laplacian and an inverse-square potential.
  • Focused on identifying both radial and nonradial solutions beyond a specific critical limit.
  • Established the existence of infinitely many radial solutions for the given equation.
  • Established the existence of infinitely many nonradial solutions, indicating a rich solution structure.

Abstract

Abstract We are interested in the multiplicity of solutions to the following scalar field equation - u - (N-2) ²4|x|² u = g (u), in RN \0\. - Δ u - (N - 2) 2 4 | x | 2 u = g (u), in R N \ 0. We establish the existence of infinitely many radial and nonradial solutions.

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Cite This Study

Bieganowski et al. (2026) studied this question.

synapsesocial.com/papers/6a1689ce0c924ddd1bd58684https://doi.org/10.1007/s13324-026-01219-1
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