On a doubly sublinear fractional $p$-Laplacian equation

Abstract

We prove a bifurcation result for a Dirichlet problem driven by the fractional $p$-Laplacian (either degenerate or singular), in which the reaction is the difference between two sublinear powers of the unknown. In our argument, a fundamental role is played by a Sobolev vs.\ H\"older minima principle, already known for the degenerate case, which here we extend to the singular case with a simpler proof.