Existence of least energy positive and nodal solutions for a quasilinear Schrödinger problem with potentials vanishing at infinity

Figueiredo, Giovany de Jesus Malcher; Moreira Neto, Sandra; Ruviaro, Ricardo

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Campo DC	Valor	Lengua/Idioma
dc.contributor.author	Figueiredo, Giovany de Jesus Malcher	-
dc.contributor.author	Moreira Neto, Sandra	-
dc.contributor.author	Ruviaro, Ricardo	-
dc.date.accessioned	2022-10-05T19:59:33Z	-
dc.date.available	2022-10-05T19:59:33Z	-
dc.date.issued	2021-09-01	-
dc.identifier.citation	FIGUEIREDO, Giovany; MOREIRA NETO, Sandra; RUVIARO, Ricardo. Existence of least energy positive and nodal solutions for a quasilinear Schrödinger problem with potentials vanishing at infinity. Journal of Mathematical Physics, v. 62, n. 9, art. 091501, 2021. DOI 10.1063/5.0015513. Disponível em: https://aip.scitation.org/doi/full/10.1063/5.0015513. Acesso em: 05 out. 2022.	pt_BR
dc.identifier.uri	https://repositorio.unb.br/handle/10482/45002	-
dc.language.iso	Inglês	pt_BR
dc.publisher	AIP Publishing	pt_BR
dc.rights	Acesso Restrito	pt_BR
dc.title	Existence of least energy positive and nodal solutions for a quasilinear Schrödinger problem with potentials vanishing at infinity	pt_BR
dc.type	Artigo	pt_BR
dc.subject.keyword	Schrödinger, Equação de	pt_BR
dc.subject.keyword	Equações quasilineares	pt_BR
dc.identifier.doi	https://doi.org/10.1063/5.0015513	pt_BR
dc.description.abstract1	In this paper, we prove the existence of at least two nontrivial solutions for a class of quasilinear problems with two non-negative and continuous potentials. Thanks to the geometries of these potentials, we are able to prove compact embeddings in some weighted Sobolev spaces, and by a minimization argument, we find a positive and a nodal (or sign-changing) (weak) solution with two nodal domains or that changes the sign exactly once in ℝ𝑁 for such problems. The nonlinearity in this problem satisfies suitable growth and monotonicity conditions, which allow this result to complement the classical results due to Liu, Wang, and Wang [Commun. Partial Differ. Equations 29, 879–901 (2004)].	pt_BR
dc.identifier.orcid	https://orcid.org/0000-0003-1697-1592	pt_BR
dc.description.unidade	Instituto de Ciências Exatas (IE)	pt_BR
dc.description.unidade	Departamento de Matemática (IE MAT)	pt_BR
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