The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1

Figueiredo, Giovany de Jesus Malcher; Pimenta, Marcos Tadeu de Oliveira; Winkert, Patrick

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DC Field	Value	Language
dc.contributor.author	Figueiredo, Giovany de Jesus Malcher	-
dc.contributor.author	Pimenta, Marcos Tadeu de Oliveira	-
dc.contributor.author	Winkert, Patrick	-
dc.date.accessioned	2026-01-29T14:46:49Z	-
dc.date.available	2026-01-29T14:46:49Z	-
dc.date.issued	2024-10-01	-
dc.identifier.citation	FIGUEIREDO, Giovany M.; PIMENTA, Marcos T. O.; WINKERT, Patrick. The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1. Nonlinear Analysis, [S.l.], v. 251, e113677, 2025. DOI: https://doi.org/10.1016/j.na.2024.113677. Disponível em: https://www.sciencedirect.com/science/article/pii/S0362546X24001962?via%3Dihub. Acesso em: 28 jan. 2026.	pt_BR
dc.identifier.uri	http://repositorio.unb.br/handle/10482/53805	-
dc.language.iso	eng	pt_BR
dc.publisher	Elsevier	pt_BR
dc.rights	Acesso Restrito	pt_BR
dc.title	The asymptotic behavior of constant sign and nodal solutions of (p,q)-Laplacian problems as p goes to 1	pt_BR
dc.type	Artigo	pt_BR
dc.subject.keyword	Comportamento assintótico	pt_BR
dc.subject.keyword	Funções de variação limitada	pt_BR
dc.subject.keyword	p-Laplaciano	pt_BR
dc.identifier.doi	https://doi.org/10.1016/j.na.2024.113677	pt_BR
dc.relation.publisherversion	https://www.sciencedirect.com/science/article/pii/S0362546X24001962?via%3Dihub	pt_BR
dc.description.abstract1	In this paper we study the asymptotic behavior of solutions to the (𝑝, 𝑞)-equation −𝛥𝑝 𝑢 − 𝛥𝑞 𝑢 = 𝑓(𝑥, 𝑢) in 𝛺, 𝑢 = 0 on 𝜕𝛺, as 𝑝 → 1 +, where 𝑁 ≥ 2, 1 < 𝑝 < 𝑞 < 1 ∗ ∶= 𝑁∕(𝑁 − 1) and 𝑓 is a Carathéodory function that grows superlinearly and subcritically. Based on a Nehari manifold treatment, we are able to prove that the (1, 𝑞)-Laplace problem given by − div ( ∇𝑢 \|∇𝑢\| ) − 𝛥𝑞 𝑢 = 𝑓(𝑥, 𝑢) in 𝛺, 𝑢 = 0 on 𝜕𝛺, has at least two constant sign solutions and one sign-changing solution, whereby the signchanging solution has least energy among all sign-changing solutions. Furthermore, the solutions belong to the usual Sobolev space 𝑊 1,𝑞 0 (𝛺) which is in contrast with the case of 1-Laplacian problems, where the solutions just belong to the space BV(𝛺) of all functions of bounded variation. As far as we know this is the first work dealing with (1, 𝑞)-Laplace problems even in the direction of constant sign solutions.	pt_BR
dc.identifier.orcid	https://orcid.org/0000-0003-1697-1592	pt_BR
dc.identifier.orcid	https://orcid.org/0000-0003-4961-3038	pt_BR
dc.identifier.orcid	https://orcid.org/0000-0003-0320-7026	pt_BR
dc.contributor.affiliation	Universidade de Brasília, Departamento de Matemática	pt_BR
dc.contributor.affiliation	Universidade Estadual Paulista, Departamento de Matemática e Computação	pt_BR
dc.contributor.affiliation	Institut für Mathematik, Technische Universität Berlin	pt_BR
dc.description.unidade	Instituto de Ciências Exatas (IE)	pt_BR
dc.description.unidade	Departamento de Matemática (IE MAT)	pt_BR
Appears in Collections:	Artigos publicados em periódicos e afins