Título:	Existence and behavior of positive solutions for a class of linearly coupled systems with discontinuous nonlinearities in RN
Autor(es):	Albuquerque, José Carlos de Santos, Gelson Conceição Gonçalves dos Figueiredo, Giovany de Jesus Malcher
E-mail do autor:	mailto:josecarlos.melojunior@ufpe.br mailto:gelsonsantos@ufpa.br mailto:giovany@unb.br
ORCID:	https://orcid.org/0000-0003-2273-6054 https://orcid.org/0000-0003-1697-1592
Assunto:	Sistemas linearmente acoplados Lipschitz, Função de Soluções positivas
Data de publicação:	8-Mar-2021
Editora:	Springer Nature
Referência:	ALBUQUERQUE, José Carlos de; SANTOS, Gelson G. dos; FIGUEIREDO, Giovany M. Existence and behavior of positive solutions for a class of linearly coupled systems with discontinuous nonlinearities in RN. Journal of Fixed Point Theory and Applications, v. 23, n.2, maio 2021. DOI 10.1007/s11784-021-00858-0. Disponível em: https://link.springer.com/article/10.1007/s11784-021-00858-0. Acesso em: 26 out. 2022.
Abstract:	In 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.
DOI:	https://doi.org/10.1007/s11784-021-00858-0
Versão da editora:	https://link.springer.com/article/10.1007/s11784-021-00858-0
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