Spectral analysis of higher-order differential operators II: Fourth-order equations

被引：30
|
作者：
Remling, C [1 ]
机构：
[1] Univ Osnabruck, Fachbereich Math Informat, D-49069 Osnabruck, Germany
来源：
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 1999年 / 59卷
关键词：
D O I：
10.1112/S0024610799007012
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate the location and nature of the spectrum of the fourth-order self-adjoint equation (p(0)y ")" + (p(1)y')' + qy = zwy subject to certain asymptotic assumptions on the coefficients. The main tools are the theory of asymptotic integration and the Titchmarsh-Weyl M-matrix. Asymptotic integration yields asymptotic formulae for the solutions of the differential equation which are then used to derive properties of the M-matrix. The characterisation of spectral properties in terms of the boundary behaviour of M leads to the desired results.
引用
收藏
页码：188 / 206
页数：19
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