论文标题
对于Dirichlet条件的分数P-Laplacian的最佳可溶性
Optimal solvability for the fractional p-Laplacian with Dirichlet conditions
论文作者
论文摘要
我们研究了由分数p-laplacian驱动的非线性，非局部差异问题，涉及（p-1） - 公共反应。通过薄弱的比较原则，我们证明了解决方案的独特性。同样，将问题与同一操作员的“渐近”加权特征值问题进行比较，我们证明了解决方案的必要条件。我们的工作将由于Brezis-Oswald和Diaz-Saa而扩展到了准线性非局部框架。
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 and Diaz-Saa to the quasilinear nonlocal framework.
