scholarly journals A limit-point criterion for a class of Sturm-Liouville operators defined in ${L^p}$ spaces

2004 ◽  
Vol 132 (08) ◽  
pp. 2273-2273
Author(s):  
R. C. Brown
Keyword(s):  
Limit Point ◽  
Sturm Liouville ◽  
Liouville Operators

Criteria of limit‐point case for conformable fractional Sturm‐Liouville operators

2019 ◽  
Vol 43 (5) ◽  
pp. 2548-2557 ◽  
Author(s):  
Zhaowen Zheng ◽  
Huixin Liu ◽  
Jinming Cai ◽  
Yanwei Zhang
Keyword(s):  
Limit Point ◽  
Sturm Liouville ◽  
Limit Point Case ◽  
Liouville Operators

m (λ)-functions for complex Sturm-Liouville operators

1980 ◽  
Vol 86 (3-4) ◽  
pp. 275-289 ◽  
Author(s):  
David Race
Keyword(s):  
Limit Point ◽  
Limit Circle ◽  
Limit Circle Case ◽  
Separated Boundary Conditions ◽  
Sturm Liouville ◽  
Limit Point Case ◽  
Complex Valued ◽  
Well Posed ◽  
Circle Case ◽  
Liouville Operators

SynopsisIn this paper, the formally J-symmetric Sturm-Liouville operator with complex-valued coefficients is considered and a generalisation of the Weyl limit-point, limit-circle dichotomy is sought by means of m (λ )-functions. These functions are then used to give an explicit description of all the associated J-selfadjoint operators with separated boundary conditions in the limit-circle case. A formulation of the eigenvalues of these operators, and a characterisation of which extensions are non-well-posed, are also found. Finally, the limit-point case is studied, mainly by means of an example.

scholarly journals Partial inverse problems for quadratic differential pencils on a graph with a loop

2020 ◽  
Vol 28 (3) ◽  
pp. 449-463 ◽  
Author(s):  
Natalia P. Bondarenko ◽  
Chung-Tsun Shieh
Keyword(s):  
Inverse Problems ◽  
A Priori ◽  
Spectral Characteristics ◽  
The Other ◽  
Boundary Edge ◽  
Partial Inverse ◽  
Quadratic Pencil ◽  
Sturm Liouville ◽  
Differential Pencils ◽  
Liouville Operators

AbstractIn this paper, partial inverse problems for the quadratic pencil of Sturm–Liouville operators on a graph with a loop are studied. These problems consist in recovering the pencil coefficients on one edge of the graph (a boundary edge or the loop) from spectral characteristics, while the coefficients on the other edges are known a priori. We obtain uniqueness theorems and constructive solutions for partial inverse problems.

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