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

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*.