Existence and behavior of positive solutions for a class of linearly coupled systems with discontinuous nonlinearities in RN

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Autor(es): dc.contributormailto:josecarlos.melojunior@ufpe.br-
Autor(es): dc.contributormailto:gelsonsantos@ufpa.br-
Autor(es): dc.contributormailto:giovany@unb.br-
Autor(es): dc.creatorAlbuquerque, José Carlos de-
Autor(es): dc.creatorSantos, Gelson Conceição Gonçalves dos-
Autor(es): dc.creatorFigueiredo, Giovany de Jesus Malcher-
Data de aceite: dc.date.accessioned2024-10-23T16:02:06Z-
Data de disponibilização: dc.date.available2024-10-23T16:02:06Z-
Data de envio: dc.date.issued2022-10-25-
Data de envio: dc.date.issued2022-10-25-
Data de envio: dc.date.issued2021-03-08-
Fonte completa do material: dc.identifierhttps://repositorio.unb.br/handle/10482/45071-
Fonte completa do material: dc.identifierhttps://doi.org/10.1007/s11784-021-00858-0-
Fonte completa do material: dc.identifierhttps://orcid.org/0000-0003-2273-6054-
Fonte completa do material: dc.identifierhttps://orcid.org/0000-0003-1697-1592-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/898240-
Descrição: dc.descriptionIn this paper we are concerned with existence and behavior of positive solutions to the following class of linearly coupled elliptic systems with discontinuous nonlinearities −Δu+V1(x)u=H(u−β)f1(u)+a(x)v,−Δv+V2(x)v=H(v−β)f2(v)+a(x)u,u,v∈D1,2(RN)∩W2,2loc(RN),in RN,in RN,(S)β where β≥0, N≥3, V1,V2, a:RN→R are positive potentials, which can vanish at infinity, f1,f2:R→R are continuous functions and H is the Heaviside function, i.e, H(t)=0 if t≤0, H(t)=1 if t>0. We use a suitable nonsmooth truncation, for systems, to apply a version of the penalization method of Del Pino and Felmer (Calc Var Partial Differ Equ 4:121–137, 1996) combined with the Mountain Pass Theorem for locally Lipschitz functional to obtain a positive solution (uβ,vβ) of (S)β in multivalued sense. In addition, we show that (uβ,vβ)→(u,v) in D1,2(RN)×D1,2(RN) as β→0+, where (u, v) is a positive solution of the continuous system (S)0 in strong sense.-
Publicador: dc.publisherSpringer Nature-
Relação: dc.relationhttps://link.springer.com/article/10.1007/s11784-021-00858-0-
Direitos: dc.rightsAcesso Restrito-
Palavras-chave: dc.subjectSistemas linearmente acoplados-
Palavras-chave: dc.subjectLipschitz, Função de-
Palavras-chave: dc.subjectSoluções positivas-
Título: dc.titleExistence and behavior of positive solutions for a class of linearly coupled systems with discontinuous nonlinearities in RN-
Tipo de arquivo: dc.typelivro digital-
Aparece nas coleções:Repositório Institucional – UNB

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