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

Silvia Frassu and Antonio Iannizzotto ()
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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

Mathematics, 2023, vol. 11, issue 2, 1-18

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 * .

Keywords: fractional p -Laplacian; bifurcation; critical point theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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