Topological structure of the solution set for a fractional p-Laplacian problem with singular nonlinearity

Abstract

We establish the existence of connected components of positive solutions for the equation \( (-\Delta_p)^s u = \lambda f(u)\), under Dirichlet boundary conditions, where the domain is a bounded in \(\mathbb{R}^N\) and has smooth boundary, \((-\Delta_p)^s\) is the fractional p-Laplacian operator, and \(f:(0,\infty) \to \mathbb{R}\) is a continuous function which may blow up to \(\pm \infty\) at the origin.