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

• Autorzy: Yongxiang Li , Huanhuan Zhang
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47H11: Degree theory
• 35J25: Boundary value problems for second-order elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2016
• Tom: 116
• Numer: 1
• Strony: 67-78

Daty

wydano

2016

Twórcy

autor

Yongxiang Li

• Department of Mathematics, Northwest Normal University, Lanzhou 730070, People's Republic of China

autor

Huanhuan Zhang

• Department of Mathematics, Northwest Normal University, Lanzhou 730070, People's Republic of China

Identyfikatory

DOI

10.4064/ap3633-12-2015