(American Institute of Mathematical Sciences, 2025-12-01) Ortega García, Alejandro; Vilasi, Luca; Wang, Youjun
We analyze the existence and multiplicity of positive solutions to a nonlocal elliptic problem involving the spectral fractional Laplacian endowed with homogeneous mixed Dirichlet-Neumann boundary conditions and
weighted critical nonlinearities. By means of variational methods and the Nehari manifold approach, we deduce the existence of multiple positive solutions under some assumptions on the behavior of the weight function around its maximum points. In this way, we extend and improve the results in [19], dealing with the Dirichlet problem for the classical Laplacian, to the nonlocal setting with mixed boundary conditions.
