Homogenization of the Spectral Problem for Periodic Elliptic Operators with Sign-Changing Density Function

被引：0
作者：
Sergey A. Nazarov
Iryna L. Pankratova
Andrey L. Piatnitski
机构：
[1] Institute for Problems in Mechanical Engineering RAS,
[2] Narvik University College,undefined
[3] Ecole Polytechnique CNRS,undefined
[4] P. N. Lebedev Physical Institute RAS,undefined
来源：
Archive for Rational Mechanics and Analysis | 2011年 / 200卷
关键词：
Dirichlet Problem; Elliptic Operator; Spectral Problem; Negative Eigenvalue; Essential Spectrum;
D O I：
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中图分类号：
学科分类号：
摘要：
The paper deals with the asymptotic behaviour of spectra of second order self-adjoint elliptic operators with periodic rapidly oscillating coefficients in the case when the density function (the factor on the spectral parameter) changes sign. We study the Dirichlet problem in a regular bounded domain and show that the spectrum of this problem is discrete and consists of two series, one of them tending towards +∞ and another towards −∞. The asymptotic behaviour of positive and negative eigenvalues and their corresponding eigenfunctions depends crucially on whether the average of the weight function is positive, negative or equal to zero. We construct the asymptotics of eigenpairs in all three cases.
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页码：747 / 788
页数：41
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