2019
DOI: 10.1007/s10231-019-00906-0
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Asymptotic behavior and existence of solutions for singular elliptic equations

Abstract: We study the asymptotic behavior, as γ tends to infinity, of solutions for the homogeneous Dirichlet problem associated to singular semilinear elliptic equations whose model iswhere Ω is an open, bounded subset of R N and f is a bounded function. We deal with the existence of a limit equation under two different assumptions on f : either strictly positive on every compactly contained subset of Ω or only nonnegative. Through this study we deduce optimal existence results of positive solutions for the homogeneou… Show more

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Cited by 13 publications
(6 citation statements)
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“…which, for = 0, was extensively studied in the past, see for instance [1,2,3,20,25]. The previous discussion could be formalized and the existence and uniqueness results given in the current paper could provide information regarding problem (1.4).…”
mentioning
confidence: 76%
“…which, for = 0, was extensively studied in the past, see for instance [1,2,3,20,25]. The previous discussion could be formalized and the existence and uniqueness results given in the current paper could provide information regarding problem (1.4).…”
mentioning
confidence: 76%
“…We are going to verify the following estimates in a similar way to previous studies. 23,25 Lemma 3.2. Suppose that u n is the solution to problem (3.1) given by Lemma 3.1, and for every…”
Section: Approximation Problemmentioning
confidence: 99%
“…If p = 2 and g(s) ∼ s −θ one may refer to [12,8,9,32,33] and references therein, while the case p > 1 has also been considered ( [54,53,20]). Observe that, in any cases, the threshold θ = 1 is shown to be critical in order to get global finite energy solutions for a general nonnegative datum f (see also the discussion in [27]).…”
Section: Introductionmentioning
confidence: 99%