Existence of positive radial solutions for the elliptic equations on an exterior domain

Yongxiang Li; Huanhuan Zhang

Annales Polonici Mathematici, Tome 116 (2016), p. 67-78 / Harvested from The Polish Digital Mathematics Library

Résumé

We discuss the existence of positive radial solutions of the semilinear elliptic equation ⎧-Δu = K(|x|)f(u), x ∈ Ω ⎨αu + β ∂u/∂n = 0, x ∈ ∂Ω, ⎩ $l i m_{| x | \to \infty} u (x) = 0$ , where $Ω = x \in ℝ^{N} : | x | > r ₀$ , N ≥ 3, K: [r₀,∞) → ℝ⁺ is continuous and $0 < \int_{r ₀}^{\infty} r K (r) d r < \infty$ , f ∈ C(ℝ⁺,ℝ⁺), f(0) = 0. Under the conditions related to the asymptotic behaviour of f(u)/u at 0 and infinity, the existence of positive radial solutions is obtained. Our conditions are more precise and weaker than the superlinear or sublinear growth conditions. Our discussion is based on the fixed point index theory in cones.

Publié le : 2016-01-01

Zbl 1338.35148

EUDML-ID : urn:eudml:doc:280889

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     author = {Yongxiang Li and Huanhuan Zhang},
     title = {Existence of positive radial solutions for the elliptic equations on an exterior domain},
     journal = {Annales Polonici Mathematici},
     volume = {116},
     year = {2016},
     pages = {67-78},
     zbl = {1338.35148},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3633-12-2015}
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Yongxiang Li; Huanhuan Zhang. Existence of positive radial solutions for the elliptic equations on an exterior domain. Annales Polonici Mathematici, Tome 116 (2016) pp. 67-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3633-12-2015/