Ortega García, AlejandroVilasi, LucaWang, Youjun2026-02-252026-02-252025-12-01Ortega, Alejandro, Vilasi, Luca, Wang, Youjun (2025). Positive solutions for a weighted critical problem with mixed boundary conditions. Discrete and Continuous Dynamical Systems 35, 153-178. http://dx.doi.org/10.3934/dcdsb.20260081531-3492http://dx.doi.org/10.3934/dcdsb.2026008https://hdl.handle.net/20.500.14468/31953The registered version of this article, first published in “Discrete and Continuous Dynamical Systems 35 (2025), 153-178", is available online at the publisher's website: American Institute of Mathematical Sciences, http://dx.doi.org/10.3934/dcdsb.2026008La versión registrada de este artículo, publicado por primera vez en “Discrete and Continuous Dynamical Systems 35 (2025), 153-178", está disponible en línea en el sitio web del editor: American Institute of Mathematical Sciences, http://dx.doi.org/10.3934/dcdsb.2026008We 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.eninfo:eu-repo/semantics/closedAccess1202 Análisis y análisis funcionalartículoFractional LaplacianMixed boundary conditionsCritical Sobolev exponentMultiplicity of solutionsVariational methodsNehari manifold1553-524X