A sharp Sobolev inequality and its applications to an indefinite elliptic equation with Neumann boundary conditions. (August 2020) - de Souza, Manassés; Felix, Diego D.; de Medeiros, Everaldo S.
Abstract: In this paper, we prove a sharp weighted Sobolev inequality on the upper half-space. As a consequence of this inequality we derive some existence, nonexistence and multiplicity results to a class of indefinite semilinear elliptic equations with Neumann boundary conditions.