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Título : On multiplicity and concentration behavior of solutions for a critical system with equations in divergence form
Autor : 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
Fecha de publicación : 28-jul-2020
Editorial : Science Direct
Citación : 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
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