Bueno, H.Ercole, GreyFerreira, Wenderson MarquesSantos, Antônio Zumpano Pereira2015-03-122015-03-122008BUENO, 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. 2015.0022-247Xhttp://www.repositorio.ufop.br/handle/123456789/4597We 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.en-USLaplacianNonlocal coefficientExistence and multiplicity of positive solutionsArtigo publicado em periodicoO periódico Journal of Mathematical Analysis and Applications concede permissão para depósito do artigo no Repositório Institucional da UFOP. Número da licença: 3584830060213.https://doi.org/10.1016/j.jmaa.2008.01.001