Curve-Like Concentration Layers for a Singularly Perturbed Nonlinear Problem with Critical Exponents
Curve-Like Concentration Layers for a Singularly Perturbed Nonlinear Problem with Critical Exponents
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DOI：
10.1080/03605302.2013.851215
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发表时间：
2014-05
影响因子：
1.9
通讯作者：
M. Musso;Jun Yang
中科院分区：
文献类型：
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作者：
M. Musso;Jun Yang
本文考虑以下问题，其中Ω是一个有界光滑域，p是n - 1维的临界Sobolev指数，即p = (n + 1)/(n - 3), λ > 0。我们证明，如果n≥8，那么对于一个小的正参数λ序列，问题允许一个正解集中在连接Ω边界两点的非退化段上。
In this paper we consider the following problem where Ω is a bounded smooth domain in ℝ n and p is the critical Sobolev exponent in dimension n − 1, namely p = (n + 1)/(n − 3), ϵ > 0. We show that, if n ≥ 8, then for a sequence of the small positive parameter ϵ, the problem admits a positive solution concentrating along a nondegenerate segment connecting two points of the boundary of Ω.