Fractional Dirichlet problems with singular and non-locally convective reaction

2024/11/17 by Laura Gambera, Gambera, Laura, S. Marano +1 · 1 citation
Mathematics · #35D30 #35J60 #35J75 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2411.11026

openalex publication_date 2024/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Differential inclusion systems with fractional competing operator and multivalued fractional convection term

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