Titre:	On multiplicity and concentration behavior of solutions for a critical system with equations in divergence form
Auteur(s):	Figueiredo, Giovany de Jesus Malcher Argomedo Salirrosas, Segundo Manuel
metadata.dc.contributor.email:	mailto:giovany@unb.br mailto:semaarsa@gmail.com
Assunto::	Schrödinger, Equação de Sistemas críticos elípticos Ljusternik-Schnirelmann, Teoria de Soluções positivas
Date de publication:	28-jui-2020
Editeur:	Science Direct
Référence bibliographique:	FIGUEIREDO, Giovany M.; A. SALIRROSAS, Segundo Manuel. On multiplicity and concentration behavior of solutions for a critical system with equations in divergence form. Journal of Mathematical Analysis and Applications, v. 494, n. 1, art. 124446, fev. 2021. DOI 10.1016/j.jmaa.2020.124446. Disponível em: https://www.sciencedirect.com/science/article/pii/S0022247X20306089?via%3Dihub. Acesso em: 19 out. 2022.
Abstract:	We consider the system −ε2div(a(x)∇u) + u = Qu(u, v) + 1 2∗ Ku(u, v) in RN , −ε2div(b(x)∇v) + v = Qv (u, v) + 1 2∗ Kv (u, v) in RN , u, v ∈ H1(RN ), u(x), v(x) > 0 for each x ∈ RN where ∗ = 2N/(N − 2), N ≥ 3, ε > 0, a and b are positive continuous potentials, and Q and K are homogeneous function with K having critical growth. We obtain existence of a ground state solution and relate the number of solutions with the topology of the set where the potentials a and b attain their minima. We also show that at the maximum points of each solution, the potentials a and b converge to their points of minima points when ε converges to zero.
DOI:	https://doi.org/10.1016/j.jmaa.2020.124446
metadata.dc.relation.publisherversion:	https://www.sciencedirect.com/science/article/pii/S0022247X20306089?via%3Dihub
Collection(s) :	Artigos publicados em periódicos e afins

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