The limit-point/limit-circle classification for ordinary differential equations with distributional coefficients

被引：0

作者：

Bhardwaj, Varun ^{[1
]}

Weikard, Rudi ^{[1
]}

机构：

[1] Univ Alabama Birmingham, Dept Math, Birmingham, AL 35294 USA

来源：

DOCUMENTA MATHEMATICA | 2024年 / 29卷

关键词：

limit-point/limit-circle; distributional coefficients; STURM;

D O I：

10.4171/DM/954

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the limit-point/limit-circle classification for the differential equation Ju' + qu = lambda wu where J = ( [GRAPHICS] and q and w are matrices whose entries are distributions of order zero with 1 0 q Hermitian and w non-negative. We identify the situations when the classical alternative of Weyl works and when it fails.

引用

页码：747 / 762

页数：16

共 9 条

[1]

Coddington EarlA., 1955, THEORY ORDINARY DIFF

[2] WEYL-TITCHMARSH THEORY FOR STURM-LIOUVILLE OPERATORS WITH DISTRIBUTIONAL POTENTIALS [J].

Eckhardt, Jonathan ;

Gesztesy, Fritz ;

Nichols, Roger ;

Teschl, Gerald .

OPUSCULA MATHEMATICA, 2013, 33 (03) :467-563

[3] Charles Sturm and the development of Sturm-Liouville theory in the years 1900 to 1950 [J].

Everitt, WN .

Sturm-Liouville Theory: Past and Present, 2005, :45-74

[4] Spectral theory for systems of ordinary differential equations with distributional coefficients [J].

Ghatasheha, Ahmed ;

Weikard, Rudi .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 268 (06) :2752-2801

[5] On the deficiency indices and self-adjointness of symmetric Hamiltonian systems [J].

Lesch, M ;

Malamud, M .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 189 (02) :556-615

[6] STURM AND LIOUVILLE WORK ON ORDINARY LINEAR-DIFFERENTIAL EQUATIONS - THE EMERGENCE OF STURM-LIOUVILLE THEORY [J].

LUTZEN, J .

ARCHIVE FOR HISTORY OF EXACT SCIENCES, 1984, 29 (04) :309-376

[7] Green's Functions for First-Order Systems of Ordinary Differential Equations without the Unique Continuation Property [J].

Redolfi, Steven ;

Weikard, Rudi .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2022, 94 (02)

[8]

Titchmarsh E. C., 1962, Eigenfunction expansions associated with second-order differential equations

[9] Ordinary differential equations with singularities and the associated developments in arbitrary functions [J].

Weyl, H .

MATHEMATISCHE ANNALEN, 1910, 68 :220-269

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