Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 60, pp. 1-19.

Title: Topological structure of the solution set for a fractional p-Laplacian problem
 with singular nonlinearity
       
Authors: Marcos R. Marcial (Univ. Federal de Ouro Preto, MG, Brazil)
         Olimpio H. Miyagaki (Univ. Federal de Sao Carlos, SP, Brazil)
         Gilberto A. Pereira (Univ. Federal de Ouro Preto, MG, Brazil)

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.

Submitted December 8, 2021. Published August 11, 2022.
Math Subject Classifications: 35A16, 35B65, 35J75, 35J92.
Key Words: Monotonicity methods; singular problems; regularity; 
          fractional p-laplacian operator.