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Quasilinear Fractional Neumann Problems

Author

Listed:
  • Dimitri Mugnai

    (Department of Ecological and Biological Sciences, University of Tuscia, Largo dell’Università, 01100 Viterbo, Italy
    These authors contributed equally to this work.)

  • Edoardo Proietti Lippi

    (Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
    These authors contributed equally to this work.)

Abstract

We study an elliptic quasilinear fractional problem with fractional Neumann boundary conditions, proving an existence and multiplicity result without assuming the classical Ambrosetti–Rabinowitz condition. Improving previous results, we also provide the weak formulation of solutions without regularity assumptions and we provide an example, even in the linear case, for which no regularity can indeed be assumed.

Suggested Citation

  • Dimitri Mugnai & Edoardo Proietti Lippi, 2024. "Quasilinear Fractional Neumann Problems," Mathematics, MDPI, vol. 13(1), pages 1-24, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:85-:d:1555697
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    References listed on IDEAS

    as
    1. Dipierro, Serena & Valdinoci, Enrico, 2021. "Description of an ecological niche for a mixed local/nonlocal dispersal: An evolution equation and a new Neumann condition arising from the superposition of Brownian and Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 575(C).
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