Blowing-up of principal eigenvalues for Neumann boundary conditions
Blowing-up of principal eigenvalues for Neumann boundary conditions
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DOI：
10.1017/s0308210506000060
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发表时间：
2007-06
期刊：
影响因子：
--
通讯作者：
K. Umezu
中科院分区：
文献类型：
--
作者：
K. Umezu
本文研究了具有不定权函数和Neumann边界条件的线性椭圆型特征值问题唯一正主特征值的爆破性质。基于唯一正主特征值的变分特征，讨论了爆破性质的充分必要条件。构造了一个反例，证明了在Dirichlet边界条件下已知的爆破性质的充分必要条件在Neumann边界条件下不再成立。
This paper studies blowing-up properties of a unique positive principal eigenvalue for a linear elliptic eigenvalue problem with an indefinite weight function and Neumann boundary condition. Necessary and sufficient conditions for the blowing-up property are discussed, based on the variational characterization of the unique positive principal eigenvalue. A counterexample is constructed, which shows that a known necessary and sufficient condition for the blowing-up property in the Dirichlet boundary condition case no longer remains true in the Neumann case.