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∗.
Bifurcation-Type Results for the Fractional p-Laplacian with Parametric Nonlinear Reaction
Frassu S.;Iannizzotto A.
2023-01-01
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∗.
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