Pohozaev-type identities for a pseudo-relativistic schrodinger operator and applications.

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.creatorBueno, Hamilton Prado-
Autor(es): dc.creatorPereira, Gilberto de Assis-
Autor(es): dc.creatorMedeiros, Aldo Henrique de Souza-
Data de aceite: dc.date.accessioned2025-08-21T15:24:42Z-
Data de disponibilização: dc.date.available2025-08-21T15:24:42Z-
Data de envio: dc.date.issued2023-08-18-
Data de envio: dc.date.issued2023-08-18-
Data de envio: dc.date.issued2019-
Fonte completa do material: dc.identifierhttp://www.repositorio.ufop.br/jspui/handle/123456789/17266-
Fonte completa do material: dc.identifierhttps://www.tandfonline.com/doi/full/10.1080/17476933.2021.1931152-
Fonte completa do material: dc.identifierhttps://doi.org/10.1080/17476933.2021.1931152-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/1013715-
Descrição: dc.descriptionIn this paper we prove a Pohozaev-type identity for both the prob- lem (−∆ + m2 ) su = f(u) in RN and its harmonic extension to R N+1 + when 0 < s < 1. So, our setting includes the pseudo-relativistic operator √ −∆ + m2 and the results showed here are original, to the best of our knowledge. The identity is first obtained in the extension setting and then “translated” into the original problem. In order to do that, we develop a specific Fourier trans- form theory for the fractionary operator (−∆ + m2 ) s , which lead us to define a weak solution u of the original problem if the identity (S) Z RN (−∆ + m2 ) s/2u(−∆ + m2 ) s/2 vdx = Z RN f(u)vdx is satisfied by all v ∈ Hs (RN ). The obtained Pohozaev-type identity is then applied to prove both a result of nonexistence of solution to the case f(u) = |u| p−2u if p ≥ 2 ∗ s and a result of existence of a ground state, if f is modeled by κu3/(1+u 2 ), for a constant κ. In this last case, we apply the Nehari-Pohozaev manifold introduced by D. Ruiz. Finally, we prove that positive solutions of (−∆ + m2 ) su = f(u) are radially symmetric and decreasing with respect to the origin, if f is modeled by functions like t α, α ∈ (1, 2 ∗ s − 1) or tln t.-
Formato: dc.formatapplication/pdf-
Idioma: dc.languageen-
Direitos: dc.rightsrestrito-
Título: dc.titlePohozaev-type identities for a pseudo-relativistic schrodinger operator and applications.-
Aparece nas coleções:Repositório Institucional - UFOP

Não existem arquivos associados a este item.