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arXiv · 2411.11026

Fractional Dirichlet problems with singular and non-locally convective reaction

Laura Gambera·Salvatore A. Marano
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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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Laura Gambera, Salvatore A. Marano. 2024-11-17. Fractional Dirichlet problems with singular and non-locally convective reaction. https://arxiv.org/abs/2411.11026

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