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arXiv · 2101.05535

On the logistic equation for the fractional p-Laplacian

Antonio Iannizzotto·Sunra Mosconi·Nikolaos S. Papageorgiou
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Abstract

We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, with a logistic type reaction depending on a positive parameter. In the subdiffusive and equidiffusive cases, we prove existence and uniqueness of the positive solution when the parameter lies in convenient intervals. In the superdiffusive case, we establish a bifurcation result. A new strong comparison result, of independent interest, plays a crucial role in the proof of such bifurcation result.

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Antonio Iannizzotto, Sunra Mosconi, Nikolaos S. Papageorgiou. 2021-01-14. On the logistic equation for the fractional p-Laplacian. https://arxiv.org/abs/2101.05535

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