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Three Weak Solutions for a Critical Non-Local Problem with Strong Singularity in High Dimension

Author

Listed:
  • Gabriel Neves Cunha

    (Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia 74001-970, Brazil)

  • Francesca Faraci

    (Department of Mathematics and Computer Sciences, University of Catania, 95125 Catania, Italy)

  • Kaye Silva

    (Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia 74001-970, Brazil)

Abstract

In this paper, we deal with a strongly singular problem involving a non-local operator, a critical nonlinearity, and a subcritical perturbation. We apply techniques from non-smooth analysis to the energy functional, in combination with the study of the topological properties of the sublevels of its smooth part, to prove the existence of three weak solutions: two points of local minimum and a third one as a mountain pass critical point.

Suggested Citation

  • Gabriel Neves Cunha & Francesca Faraci & Kaye Silva, 2024. "Three Weak Solutions for a Critical Non-Local Problem with Strong Singularity in High Dimension," Mathematics, MDPI, vol. 12(18), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2910-:d:1480569
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