Sturm-Liouville problems with singular non-selfadjoint boundary conditions

被引：5

作者：

Eberhard, W

Freiling, G ^{[1
]}

Zettl, A

机构：

[1] Univ Duisburg Essen, Dept Math, D-47048 Duisburg, Germany

[2] No Illinois Univ, Dept Math, De Kalb, IL 60115 USA

来源：

MATHEMATISCHE NACHRICHTEN | 2005年 / 278卷 / 12-13期

关键词：

singular Sturm-Liouville problems; Birkhoff-regular problems; asymptotic behavior of eigenvalues; eigenfunction expansion;

D O I：

10.1002/mana.200310318

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Singular boundary conditions are formulated for non-selfadjoint Sturm-Liouville problems which are limit-circle in a very general sense. The characteristic determinant is constructed and it is shown that it can be used to extend the Birkhoff theory for so called "Birkhoff regular boundary conditions" to the singular case. This is illustrated for a class of singular Birkhoff-regular problems; in particular we prove for this class an asymptotic formula for the eigenvalues and an expansion theorem. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

引用

页码：1509 / 1523

页数：15

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