Irregular boundary value problem for the Sturm–Liouville operator

2017 ◽  
Vol 53 (8) ◽  
pp. 1021-1028
Author(s):  
A. S. Makin ◽  
T. E. Moiseev
Keyword(s):  
Boundary Value Problem ◽  
Liouville Operator ◽  
Boundary Value ◽  
Irregular Boundary ◽  
Sturm Liouville

scholarly journals Identification of the Domain of the Sturm–Liouville Operator on a Star Graph

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1210
Author(s):  
Baltabek Kanguzhin ◽  
Ghulam Hazrat Aimal Aimal Rasa ◽  
Zhalgas Kaiyrbek
Keyword(s):  
Boundary Value Problem ◽  
Finite Number ◽  
Liouville Operator ◽  
Boundary Value ◽  
Star Graph ◽  
Linear Forms ◽  
Symmetric Star ◽  
Sturm Liouville ◽  
Definition Of ◽  
Boundary Form

This article is devoted to the unique recovering of the domain of the Sturm–Liouville operator on a star graph. The domain of the Sturm–Liouville operator is uniquely identified from the set of spectra of a finite number of specially selected canonical problems. In the general case, the domain of the definition of the original operator can be specified by integro-differential linear forms. In the case when the domain of the Sturm–Liouville operator on a star graph corresponds to the boundary value problem, it is sufficient to choose only finite parts of the spectra of canonical problems for a unique identification of the boundary form. Moreover, the above statement is valid only for a symmetric star graph.

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