Czasopismo
Tytuł artykułu
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![https://www.impan.pl/download/pdf/ap3633-12-2015 [zdalny]](images/mime-icons/pdf.gif "ap3633-12-2015.pdf"){kind=icon}
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Języki publikacji
Abstrakty
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,
⎩$lim_{|x|→∞} u(x) = 0$,
where $Ω = {x ∈ ℝ^{N}: |x| > r₀}$, N ≥ 3, K: [r₀,∞) → ℝ⁺ is continuous and $0 < ∫_{r₀}^{∞} rK(r)dr < ∞$, 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.
⎧-Δu = K(|x|)f(u), x ∈ Ω
⎨αu + β ∂u/∂n = 0, x ∈ ∂Ω,
⎩$lim_{|x|→∞} u(x) = 0$,
where $Ω = {x ∈ ℝ^{N}: |x| > r₀}$, N ≥ 3, K: [r₀,∞) → ℝ⁺ is continuous and $0 < ∫_{r₀}^{∞} rK(r)dr < ∞$, 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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
67-78
Opis fizyczny
Daty
wydano
2016
Twórcy
autor
- Department of Mathematics, Northwest Normal University, Lanzhou 730070, People's Republic of China
autor
- Department of Mathematics, Northwest Normal University, Lanzhou 730070, People's Republic of China
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-ap3633-12-2015
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