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On the logistic equation for the fractional p‐Laplacian

Author

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  • Antonio Iannizzotto
  • Sunra Mosconi
  • Nikolaos S. Papageorgiou

Abstract

We consider a Dirichlet problem for a nonlinear, nonlocal equation driven by the degenerate fractional p‐Laplacian, with a logistic‐type reaction depending on a positive parameter. In the subdiffusive and equidiffusive cases, we prove existence and uniqueness of the positive solution when the parameter lies in convenient intervals. In the superdiffusive case, we establish a bifurcation result. A new strong comparison result, of independent interest, plays a crucial role in the proof of such bifurcation result.

Suggested Citation

  • Antonio Iannizzotto & Sunra Mosconi & Nikolaos S. Papageorgiou, 2023. "On the logistic equation for the fractional p‐Laplacian," Mathematische Nachrichten, Wiley Blackwell, vol. 296(4), pages 1451-1468, April.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:4:p:1451-1468
    DOI: 10.1002/mana.202100025
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    References listed on IDEAS

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    1. Kanishka Perera & Marco Squassina & Yang Yang, 2016. "Bifurcation and multiplicity results for critical fractional p-Laplacian problems," Mathematische Nachrichten, Wiley Blackwell, vol. 289(2-3), pages 332-342, February.
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    Cited by:

    1. Leszek Gasiński & Nikolaos S. Papageorgiou, 2024. "On an Anisotropic Logistic Equation," Mathematics, MDPI, vol. 12(9), pages 1-13, April.

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