Special Session 66: Geometric insights in Partial Differential Equations: advances and challenges

On a weighted Brezis-Nirenberg-type fractional problem with mixed boundary conditions
Luca Vilasi
University of Messina
Italy
Co-Author(s):    Alejandro Ortega, Youjun Wang
Abstract:
We consider an elliptic problem governed by the spectral fractional Laplacian with mixed Dirichlet-Neumann boundary conditions, weighted critical nonlinearities and subcritical perturbations. By using variational arguments we deduce the existence of multiple positive solutions when the weight suitably behaves around its maximum points. In particular, we get different results depending on whether the Dirichlet Sobolev constant is attained or not, Our results extend and improve similar ones obtained in the local case with purely Dirichlet boundary conditions.