Title:	On a planar non-autonomous Schrödinger–Poisson system involving exponential critical growth
Authors:	Albuquerque, Francisco Sibério Bezerra Carvalho, Jonison Lucas dos Santos Figueiredo, Giovany de Jesus Malcher Medeiros, Everaldo Souto de
metadata.dc.contributor.email:	mailto:fsiberio@cct.uepb.edu.br mailto:jonison.mat@gmail.com mailto:giovany@unb.br mailto:everaldo@mat.ufpb.br
Assunto::	Schrödinger, Equação de Sistema Schrödinger–Poisson
Issue Date:	24-Jan-2021
Publisher:	Springer
Citation:	ALBUQUERQUE, F. S.; CARVALHO, J. L.; FIGUEIREDO, G. M.; MEDEIROS, E. On a planar non-autonomous Schrödinger–Poisson system involving exponential critical growth. Calculus of Variations and Partial Differential Equations, v. 60, art. 40, 2021. DOI 10.1007/s00526-020-01902-6. Disponível em: https://link.springer.com/article/10.1007/s00526-020-01902-6. Acesso em: 19 out. 2022.
Abstract:	In this paper, we investigate the existence of solutions to the planar non-autonomous Schrödinger–Poisson system {−Δu+V(|x|)u+γϕK(|x|)u=λQ(|x|)f(u), &x∈R2,Δϕ=K(|x|)u2, &x∈R2, where γ,λ are positive parameters, V, K, Q are continuous potentials, which can be unbounded or vanishing at infinity. By assuming that the nonlinearity f(s) has exponential critical growth, we derive the existence of a ground state solution to the system. A key feature of our approach is a new weighted Trudinger–Moser type inequality proved here.
DOI:	https://doi.org/10.1007/s00526-020-01902-6
metadata.dc.relation.publisherversion:	https://link.springer.com/article/10.1007/s00526-020-01902-6
Appears in Collections:	Artigos publicados em periódicos e afins

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