We study a nonlinear, nonlocal Dirichlet problem driven by the fractional p-Laplacian, involving a \((p-1)\)-sublinear reaction. By means of a weak comparison principle we prove uniqueness of the solution. Also, comparing the problem to ’asymptotic’ weighted eigenvalue problems for the same operator, we prove a necessary and sufficient condition for the existence of a solution. Our work extends classical results due to Brezis-Oswald [7] and Diaz-Saa [11] to the nonlinear nonlocal framework.

中文翻译：

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狄利克雷条件下分数 p-拉普拉斯算子的最佳可解性

我们研究由分数p拉普拉斯算子驱动的非线性、非局部狄利克雷问题，涉及\((p-1)\)次线性反应。通过弱比较原理，我们证明了解的唯一性。此外，将该问题与同一算子的“渐近”加权特征值问题进行比较，我们证明了解存在的充分必要条件。我们的工作将 Brezis-Oswald [7] 和 Diaz-Saa [11] 的经典结果扩展到非线性非局部框架。