A sharp Sobolev inequality and its applications to an indefinite elliptic equation with Neumann boundary conditions

A sharp Sobolev inequality and its applications to an indefinite elliptic equation with Neumann boundary conditions

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.

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Veröffentlicht in:Nonlinear analysis 2020-08, Vol.197, p.111840, Article 111840
Hauptverfasser: de Souza, Manassés, Felix, Diego D., de Medeiros, Everaldo S.
Format: Artikel
Sprache:eng
Schlagworte:
Boundary conditions
Elliptic functions
Half spaces
Inequality
Neumann boundary value problems
Nonlinear elliptic problems
Upper half-space
Variational methods
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Zusammenfassung: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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2020.111840