The deficiency indices of powers of second order expressions with large leading coefficient

1985 ◽  
Vol 101 (3-4) ◽  
pp. 227-235
Author(s):  
Thomas T. Read
Keyword(s):  
Large Class ◽  
Differential Expression ◽  
Limit Point ◽  
Second Order ◽  
Simple Function ◽  
Deficiency Index ◽  
Deficiency Indices

SynopsisThe deficiency index of each power of the differential expression M[y] = w−1(−(py′)′ + qy), defined on [a, ∞), is calculated exactly in terms of the behaviour of a simple function of p and w for a large class of expressions satisfying a hypothesis which requires that p be large compared with w and q. In general, not all powers of M are limit-point.

scholarly journals Stability of deficiency indices for discrete Hamiltonian systems under bounded perturbations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yan Liu ◽  
Meiru Xu
Keyword(s):  
Perturbation Theory ◽  
Hamiltonian Systems ◽  
Limit Point ◽  
Limit Circle ◽  
Linear Relations ◽  
Deficiency Indices ◽  
Bounded Perturbations

AbstractThis paper is concerned with stability of deficiency indices for discrete Hamiltonian systems under perturbations. By applying the perturbation theory of Hermitian linear relations we establish the invariance of deficiency indices for discrete Hamiltonian systems under bounded perturbations. As a consequence, we obtain the invariance of limit types for the systems under bounded perturbations. In particular, we build several criteria of the invariance of the limit circle and limit point cases for the systems. Some of these results improve and extend some previous results.

17.—The Limit-point and Limit-circle Cases for Polynomials in a Differential Operator

1975 ◽  
Vol 72 (3) ◽  
pp. 219-224 ◽  
Author(s):  
Anton Zettl
Keyword(s):  
Differential Operator ◽  
Differential Expression ◽  
Limit Point ◽  
Half Line ◽  
Limit Circle

SynopsisThis paper is concerned with the L2 classification of ordinary symmetrical differential expressions defined on a half-line [0, ∞) and obtained from taking formal polynomials of symmetric differential expression. The work generalises results in this area previously obtained by Chaudhuri, Everitt, Giertz and the author.

Odd-order differential expressions with positive supporting coefficients

1987 ◽  
Vol 105 (1) ◽  
pp. 167-192 ◽  
Author(s):  
Bernd Schultze
Keyword(s):  
Essential Spectrum ◽  
Deficiency Index ◽  
Deficiency Indices ◽  
Compact Perturbations ◽  
Odd Order ◽  
Independent Variable

SynopsisThe deficiency indices (mean deficiency index) and the essential spectrum for a class of odd order ordinary differential expressions are determined. The considered expressions are relatively bounded or relatively compact perturbations of symmetric expressions with odd order terms having as coefficients real powers of the independent variable.

Limit-point and limit-circle criteria for Sturm-Liouville equations with intermittently negative principal coefficients

1986 ◽  
Vol 103 (3-4) ◽  
pp. 215-228 ◽  
Author(s):  
W. N. Everitt ◽  
I. W. Knowles ◽  
T. T. Read
Keyword(s):  
Differential Expression ◽  
Limit Point ◽  
Limit Circle ◽  
Almost Everywhere ◽  
Sturm Liouville ◽  
Image Position

SynopsisLimit-point and limit-circle criteria are given for the generalised Sturm-Liouville differential expressionwhere(i) p, q, and w are real-valued on [a, b),(ii) p−1, q, w are locally Lebesgue integrable on [a, b),(iii) w > 0 almost everywhere on [a, b) and the principal coefficient p is allowed toassume both positive and negative values.

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