Positive Solutions to Singular Semilinear Elliptic Problems |
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Authors: | Khalifa El Mabrouk |
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Institution: | (1) Department of Mathematics, Faculty of Sciences of Monastir, 5019 Monastir, Tunisia |
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Abstract: | We obtain a characterization of all locally bounded functions p ≥ 0 for which the equation (E) Δu +p(x)ψ(u) = 0 has a positive solution in Ω vanishing on the boundary, where Ω is a domain of ℝN and ψ > 0 is a nonincreasing continuous function on ]0,∞. In particular, for Ω = ℝN with N ≥ 3, it is shown that (E) has a (unique) positive solution in ℝN which decays to zero at infinity if and only if the set {p > 0} has positive Lebesgue measure and
This condition can be replaced by if p is radial. |
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Keywords: | 35J65 35D05 31C45 |
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