Title:	Positive solutions of the prescribed mean curvature equation with exponential critical growth
Authors:	Figueiredo, Giovany de Jesus Malcher Rădulescu, Vicenţiu D.
metadata.dc.identifier.orcid:	https://orcid.org/0000-0003-1697-1592 https://orcid.org/0000-0003-4615-5537
Assunto::	Curvatura média constante Crescimento exponencial crítico Lewy–Stampacchia, Estimativa de
Issue Date:	1-Mar-2021
Publisher:	Springer Nature
Citation:	FIGUEIREDO, Giovany M.; RĂDULESCU, Vicenţiu D. Positive solutions of the prescribed mean curvature equation with exponential critical growth. Annali di Matematica, v. 200, n. 5, p. 2213–2233, out. 2021. DOI 10.1007/s10231-021-01077-7. Disponível em: https://link.springer.com/article/10.1007/s10231-021-01077-7. Acesso em: 21 out. 2022.
Abstract:	In this paper, we are concerned with the problem − div ⎛⎝⎜∇u1+|∇u|2−−−−−−−−√⎞⎠⎟=f(u) in Ω, u=0 on ∂Ω, where Ω⊂R2 is a bounded smooth domain and f:R→R is a superlinear continuous function with critical exponential growth. We first make a truncation on the prescribed mean curvature operator and obtain an auxiliary problem. Next, we show the existence of positive solutions of this auxiliary problem by using the Nehari manifold method. Finally, we conclude that the solution of the auxiliary problem is a solution of the original problem by using the Moser iteration method and Stampacchia’s estimates.
Licença::	Annali di Matematica Pura ed Applicata (1923 -) articles are published open access under a CC BY licence (Creative Commons Attribution 4.0 International licence). The CC BY licence is the most open licence available and considered the industry 'gold standard' for open access; it is also preferred by many funders. This licence allows readers to copy and redistribute the material in any medium or format, and to alter, transform, or build upon the material, including for commercial use, providing the original author is credited. Fonte: https://www.springer.com/journal/10231/how-to-publish-with-us#Fees%20and%20Funding. Acesso em: 21 out. 2022.
DOI:	https://doi.org/10.1007/s10231-021-01077-7
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