Sturm-Liouville operators with indefinite weight functions and eigenvalue depending boundary conditions

被引：12

作者：

Behrndt, J ^{[1
]}

Trunk, C ^{[1
]}

机构：

[1] Tech Univ Berlin, Math Inst, D-10623 Berlin, Germany

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2006年 / 222卷 / 02期

关键词：

boundary value problems; Sturm-Liouville operators; generalized Nevanlinna functions; operators with finitely many negative squares; definitizable operators; boundary value spaces; Weyl functions;

D O I：

10.1016/j.jde.2005.05.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a class of boundary value problems for Sturm-Liouville operators with indefinite weight functions. The spectral parameter appears nonlinearly in the boundary condition in the form of a function tau which has the property that lambda -> lambda tau (lambda) is a generalized Nevanlinna function. We construct linearizations of these boundary value problems and study their spectral properties. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：297 / 324

页数：28

共 33 条

[1] ACHIESER NI, 1968, THEORIE LINEAREN OPE
[2] BEHRNDT J, IN PRESS OPER THEORY
[3] BEHRNDT J, IN PRESS INTEGRAL EQ
[4] Elliptic eigenvalue problems with eigenparameter dependent boundary conditions
Binding, P
Hryniv, R
Langer, H
Najman, B
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2001, 174 (01) : 30 - 54
[5] STURM-LIOUVILLE PROBLEMS WITH EIGENPARAMETER DEPENDENT BOUNDARY-CONDITIONS
BINDING, PA
BROWNE, PJ
SEDDIGHI, K
[J]. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1994, 37 : 57 - 72
[6] Curgus B, 1995, OPER THEOR, V80, P90
[7] CURGUS B, 1989, J DIFFER EQUATIONS, V79, P31
[8] Curgus B., 1994, Differ. Integral Equ, V7, P1241
[9] On Weyl function and generalized resolvents of a Hermitian operator in a Krein space
Derkach, V
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 1995, 23 (04) : 387 - 415
[10] Derkach V., 1999, Methods Funct. Anal. Topology, V5, P65

← 1 2 3 4 →