2009
DOI: 10.1016/j.jde.2009.01.016
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Abstract: We study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with Singular lower order terms that have natural growth with respect to the gradient, whose model is {-Delta u + vertical bar del u vertical bar(2)/u(gamma) = f in Omega. u = 0 on partial derivative Omega. where Omega is an open bounded subset of R, gamma > 0 and f is a function which is strictly positive on every compactly contained subset of Omega. As a consequence of our main results, we prove that the conditi… Show more

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Cited by 86 publications
(83 citation statements)
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“…Once we have proved that it is bounded, under conditions of the previous lemma, we have that any solution u is continuous in Ω arguing as in [12] (see Remark 2.6 in [2] for a detailed proof).…”
Section: Lemma 22 Assume That There Existsmentioning
confidence: 86%
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“…Once we have proved that it is bounded, under conditions of the previous lemma, we have that any solution u is continuous in Ω arguing as in [12] (see Remark 2.6 in [2] for a detailed proof).…”
Section: Lemma 22 Assume That There Existsmentioning
confidence: 86%
“…Finally, we present a general result of non-existence of positive solution of a general problem using the ideas in [2]. This result will be applied to show the non-existence of positive solution of (1.1) for λ small when f (λ, u) = λu q and γ < 1 < q.…”
Section: Lemma 22 Assume That There Existsmentioning
confidence: 99%
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