Asymptotic behavior of least energy solutions for a biharmonic problem with nearly critical growth
Asymptotic behavior of least energy solutions for a biharmonic problem with nearly critical growth
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DOI：
10.3233/asy-2008-0904
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发表时间：
2009-02
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影响因子：
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通讯作者：
F. Takahashi
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文献类型：
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作者：
F. Takahashi
当ε → +0时，其中Ω是RN（N5）中的光滑有界区域，c 0 =（N − 4）（N − 2）N（N + 2），ε > 0是一个小的正参数，pε = p − ε，p =（N + 4）/（N − 4）是从Sobolev嵌入H2 → Lp+1（Ω）的观点看的临界Sobolev指数，且K ∈ C2（Ω）是给定的正函数。（Pε，K）的边界条件称为Navier边界条件。对于二阶Laplacian情形的问题ε n = N（N − 2）K（x）u（N+2）/（N −2）−ε in Ω，u > 0 in Ω，u = 0 on Ω，
as ε → +0, where Ω is a smooth bounded domain in RN (N 5), c0 = (N − 4)(N − 2)N (N + 2), ε > 0 is a small positive parameter, pε = p − ε, p = (N + 4)/(N − 4) is the critical Sobolev exponent from the view point of the Sobolev embedding H2 ∩ H1 0 (Ω) ↪→ Lp+1(Ω), and K ∈ C2(Ω) is a given positive function. Boundary condition of (Pε,K) is called as the Navier boundary condition. For the second-order Laplacian-case problem ⎧⎨ ⎩ −Δu = N (N − 2)K(x)u(N+2)/(N −2)−ε in Ω, u > 0 in Ω, u = 0 on ∂Ω,