Existence of multiple positive solutions of inhomogeneous semilinear elliptic problems in unbounded domains
Existence of multiple positive solutions of inhomogeneous semilinear elliptic problems in unbounded domains
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DOI：
10.1017/s0308210500020667
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
Xiping Zhu;Huan-Song Zhou
中科院分区：
文献类型：
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作者：
Xiping Zhu;Huan-Song Zhou
利用Lions [14，16]的集中-紧性方法和Ambrosetti和Rabinowitz [3]的山路定理，通过对某些逼近解序列的能量平衡的仔细考察，我们证明了在适当的f和h条件下，非齐次问题.−Δu + c2 u = λ（f（u）+ h（x）），其中x ∈ Ω（Ω是<$N，N <$3中的一个外区域）且至少有两个正解。
Synopsis By using the concentration-compactness method of Lions [14, 16] and the mountain pass theorem of Ambrosetti and Rabinowitz [3], through a careful inspection of the energy balance for some sequence of approximated solutions, we show that under suitable conditions on f and h, the inhomogeneous problem. −Δu + c2u = λ(f(u) + h(x)) for x ∈ Ω (Ω is an exterior domain in ℝN, N≧ 3) and has at least two positive solutions.