Título:	Existence and concentration of positive solutions for a critical p&q equation
Autor(es):	Costa, Gustavo Silvestre do Amaral Figueiredo, Giovany de Jesus Malcher
Assunto:	Expoente crítico Equação p&q Métodos variacionais
Data de publicação:	17-Jul-2021
Editora:	De Gruyter
Referência:	COSTA, Gustavo S.; FIGUEIREDO, Giovany M. Existence and concentration of positive solutions for a critical p&q equation. Advances in Nonlinear Analysis, [S. l.], v. 11, n.1, 2, p. 243-267, 2022. DOI: https://doi.org/10.1515/anona-2020-0190. Disponível em:https://www.degruyter.com/document/doi/10.1515/anona-2020-0190/html. Acesso em: 08 jul. 2024.
Abstract:	We show existence and concentration results for a class of p&q critical problems given by −div a ϵp|∇u| p ϵp|∇u| p−2∇u + V(z)b |u| p |u| p−2u = f(u) + |u| q*−2u in RN , where u ∈ W1,p(RN) ∩ W1,q(RN), ϵ > 0 is a small parameter, 1 < p ≤ q < N, N ≥ 2 and q* = Nq/(N − q). The potential V is positive and f is a superlinear function of C1 class. We use Mountain Pass Theorem and the penalization arguments introduced by Del Pino & Felmer’s associated to Lions’ Concentration and Compactness Principle in order to overcome the lack of compactness.
Unidade Acadêmica:	Instituto de Ciências Exatas (IE) Departamento de Matemática (IE MAT)
Licença:	Open Access. © 2021 Gustavo S. Costa and Giovany M. Figueiredo, published by De Gruyter. (CC BY) This work is licensed under the Creative Commons Attribution alone 4.0 License.
DOI:	https://doi.org/10.1515/anona-2020-0190
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