Bifurcation-type results for the fractional p-Laplacian with parametric nonlinear reaction

TL;DR

This paper investigates the existence of positive solutions for a Dirichlet problem involving the fractional p-Laplacian with a nonlinear reaction that varies with a parameter, using variational methods and bifurcation analysis.

Contribution

It provides a bifurcation-type result for positive solutions in a fractional p-Laplacian problem with parametric nonlinear reaction, including concave-convex cases.

Findings

Existence of positive solutions bifurcates from zero as parameter varies.

Application of variational methods and critical point theory.

Handles nonlinear reactions with sublinear and superlinear growth.

Abstract

We study a Dirichlet problem driven by the degenerate fractional p-Laplacian and involving a nonlinear reaction, which depends on a positive parameter. The reaction is assumed to be (p-1)-sublinear near the origin and (p-1)-superlinear at infinity (including the concave-convex case). Following a variational approach based on a combination of critical point theory and suitable truncation techniques, we prove a bifurcation-type result for the existence of positive solutions.