Electron. J. Differential Equations, Vol. 2022 (2022), No. 60, pp. 1-19.

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

Marcos R. Marcial, Olimpio H. Miyagaki, Gilberto A. Pereira

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.
DOI: https://doi.org/10.58997/ejde.2022.60

An addendum was posted on August 19, 2022. It expands Remark 2.1 and add 3 references. See the last page of this article.

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Marcos Roberto Marcial
Universidade Federal de Ouro Preto
Departamento de Matemática
35400-000 - Ouro Preto - MG, Brazil
email: mrmarcial@ufop.edu.br
Olimpio H. Miyagaki
Departmento de Matemática
Universidade Federal de São Carlos
13565-905 - São Carlos - SP, Brazil
email: olimpio@ufscar.br, ohmiyagaki@gmail.com
Gilberto A. Pereira
Universidade Federal de Ouro Preto
Departamento de Matemática
35400-000 - Ouro Preto - MG, Brazil
email: gilberto.pereira@ufop.edu.br

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