Title:	Existence of least energy positive and nodal solutions for a quasilinear Schrödinger problem with potentials vanishing at infinity
Authors:	Figueiredo, Giovany de Jesus Malcher Moreira Neto, Sandra Ruviaro, Ricardo
metadata.dc.identifier.orcid:	https://orcid.org/0000-0003-1697-1592
Assunto::	Schrödinger, Equação de Equações quasilineares
Issue Date:	1-Sep-2021
Publisher:	AIP Publishing
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.
Abstract:	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)].
metadata.dc.description.unidade:	Instituto de Ciências Exatas (IE) Departamento de Matemática (IE MAT)
DOI:	https://doi.org/10.1063/5.0015513
Appears in Collections:	Artigos publicados em periódicos e afins

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