Existence and multiplicity of positive solutions for the p-Laplacian with nonlocal coefficient.

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dc.contributor.authorBueno, H.
dc.contributor.authorErcole, Grey
dc.contributor.authorFerreira, Wenderson Marques
dc.contributor.authorSantos, Antônio Zumpano Pereira
dc.date.accessioned2015-03-12T18:48:36Z
dc.date.available2015-03-12T18:48:36Z
dc.date.issued2008
dc.description.abstractWe consider the Dirichlet problem with nonlocal coefficient given by −a(Ω|u|q dx)_pu = w(x)f (u) in a bounded, smooth domain Ω ⊂ Rn (n _ 2), where _p is the p-Laplacian, w is a weight function and the nonlinearity f (u) satisfies certain local bounds. In contrast with the hypotheses usually made, no asymptotic behavior is assumed on f . We assume that the nonlocal coefficient a(_Ω|u|q dx) (q _ 1) is defined by a continuous and nondecreasing function a : [0,∞)→[0,∞) satisfying a(t) > 0 for t > 0 and a(0) _ 0. A positive solution is obtained by applying the Schauder Fixed Point Theorem. The case a(t) = tγ/q (0 < γ < p − 1) will be considered as an example where asymptotic conditions on the nonlinearity provide the existence of a sequence of positive solutions for the problem with arbitrarily large sup norm.pt_BR
dc.identifier.citationBUENO, H. et al. Existence and multiplicity of positive solutions for the p-Laplacian with nonlocal coefficient. Journal of Mathematical Analysis and Applications, v. 343, p. 151-158, 2008. Disponível em: <http://www.sciencedirect.com/science/article/pii/S0022247X08000036>. Acesso em: 10 mar. 2015.pt_BR
dc.identifier.doihttps://doi.org/10.1016/j.jmaa.2008.01.001
dc.identifier.issn0022-247X
dc.identifier.urihttp://www.repositorio.ufop.br/handle/123456789/4597
dc.language.isoen_USpt_BR
dc.rights.licenseO periódico Journal of Mathematical Analysis and Applications concede permissão para depósito do artigo no Repositório Institucional da UFOP. Número da licença: 3584830060213.pt_BR
dc.subjectLaplacianpt_BR
dc.subjectNonlocal coefficientpt_BR
dc.subjectExistence and multiplicity of positive solutionspt_BR
dc.titleExistence and multiplicity of positive solutions for the p-Laplacian with nonlocal coefficient.pt_BR
dc.typeArtigo publicado em periodicopt_BR
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