Title:	Concentration, existence of a ground state and multiplicity of solutions for a subcritical elliptic system via penalization method
Authors:	Figueiredo, Giovany de Jesus Malcher Argomedo Salirrosas, Segundo Manuel
metadata.dc.contributor.email:	mailto:giovany@unb.br mailto:semaarsa@gmail.com
metadata.dc.identifier.orcid:	https://orcid.org/0000-0003-1697-1592 https://orcid.org/0000-0003-2570-7603
Assunto::	Sistemas elípticos Schrödinger, Equação de Ljusternik-Schnirelmann, Teoria de Soluções positivas
Issue Date:	13-Jan-2021
Publisher:	Springer
Citation:	FIGUEIREDO, Giovany M.; A. SALIRROSAS, Segundo Manuel. Concentration, existence of a ground state and multiplicity of solutions for a subcritical elliptic system via penalization method. SN Partial Differential Equations and Applications, v. 2, n. 1, art. 6, fev. 2021. DOI 10.1007/s42985-020-00064-6. Disponível em: https://link.springer.com/article/10.1007/s42985-020-00064-6. Acesso em: 21 out. 2022.
Abstract:	We consider the system −ε2 div (a(x)∇u)+u=Qu(u,v) in RN,−ε2 div (b(x)∇v)+v=Qv(u,v) in RN,u,v∈H1(RN),u(x),v(x)>0for each x∈RN, where ε>0, a and b are positive continuous potentials and Q is a p-homogeneous function with subcritical growth. In the first place we show existence of a ground state solution for this system. After that, we show existence of multiple solutions involving the category theory and the topology of the sets of minima of the potentials a and b . Finally, we show a concentration result. More precisely, we show that at the maximum points of each solution, the potentials a and b converge to their points of minimum points when ε converges to zero.
DOI:	https://doi.org/10.1007/s42985-020-00064-6
Appears in Collections:	Artigos publicados em periódicos e afins

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