Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, part II
Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, part II
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DOI：
10.1512/iumj.2004.53.2400
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发表时间：
2004-07
影响因子：
1.1
通讯作者：
A. Ambrosetti;A. Malchiodi;W. Ni
中科院分区：
文献类型：
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作者：
A. Ambrosetti;A. Malchiodi;W. Ni
在Neumann或Dirichlet边界条件下，研究了方程- e2 Δu + V(|x|)u = up，其中e > 0和p > 1在R n的球或环空中。当e趋于零时，我们证明了径向解的存在性，该解具有集中在某球附近的内一维尖峰的轮廓。特别令人感兴趣的是由诺伊曼或狄利克雷边界条件对解的浓度集的存在性和位置产生的不同或相反的影响。
We study the equation -e 2 Δu + V(|x|)u = u p , with e > 0 and p > 1, in balls or annuli of R n , under Neumann or Dirichlet boundary conditions. As e tends to zero we prove existence of radial solutions, with the profile of an interior one-dimensional spike, concentrated near some sphere. Of particular interest are the different, or opposite, effects created by the Neumann or Dirichlet boundary conditions on the existence as well as the locations of the concentration sets of solutions.