Fractional Dirichlet problems with singular and non-locally convective reaction

TL;DR

This paper establishes the existence of positive weak solutions for a fractional Dirichlet problem involving a fractional (p,q)-Laplacian with singular and non-local convective reactions, using advanced mathematical techniques.

Contribution

It introduces new existence results for fractional (p,q)-Laplacian problems with singular and non-local reactions, combining sub-super solutions and variational methods.

Findings

Proves existence of positive weak solutions.

Handles singular and non-local convective reactions.

Employs sub-super solution and variational techniques.

Abstract

In this paper, the existence of positive weak solutions to a Dirichlet problem driven by the fractional $(p,q)$-Laplacian and with reaction both weakly singular and non-locally convective (i.e., depending on the distributional Riesz gradient of solutions) is established. Due to the nature of the right-hand side, we address the problem via sub-super solution methods, combined with variational techniques, truncation arguments, as well as fixed point results.