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Bifurcation-Type Results for the Fractional p -Laplacian with Parametric Nonlinear Reaction

Author

Listed:
  • Silvia Frassu

    (Department of Mathematics and Computer Science, University of Cagliari, Via Ospedale 72, 09124 Cagliari, Italy)

  • Antonio Iannizzotto

    (Department of Mathematics and Computer Science, University of Cagliari, Via Ospedale 72, 09124 Cagliari, Italy)

Abstract

We consider a nonlinear, nonlocal elliptic equation driven by the degenerate fractional p -Laplacian with a Dirichlet boundary condition and involving a parameter λ > 0 . The reaction is of general type, including concave–convex reactions as a special case. By means of variational methods and truncation techniques, we prove that there exists λ * such that the problem has two positive solutions for λ < λ * , one solution for λ = λ * , and no solutions for λ > λ * .

Suggested Citation

  • Silvia Frassu & Antonio Iannizzotto, 2023. "Bifurcation-Type Results for the Fractional p -Laplacian with Parametric Nonlinear Reaction," Mathematics, MDPI, vol. 11(2), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:491-:d:1037909
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