Ambarzumyan-type theorem for the impulsive Sturm–Liouville operator

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ran Zhang ◽  
Chuan-Fu Yang
Keyword(s):  
Liouville Operator ◽  
Type Theorem ◽  
Sturm Liouville ◽  
Neumann Laplacian ◽  
Neumann Eigenvalues

AbstractWe prove that if the Neumann eigenvalues of the impulsive Sturm–Liouville operator {-D^{2}+q} in {L^{2}(0,\pi)} coincide with those of the Neumann Laplacian, then {q=0}.

REMARK ON ESTIMATE OF A POTENTIAL IN TERMS OF EIGENVALUES OF THE STURM–LIOUVILLE OPERATOR

2008 ◽  
Vol 22 (23) ◽  
pp. 2177-2180
Author(s):  
EVGENY KOROTYAEV
Keyword(s):  
Boundary Conditions ◽  
Liouville Operator ◽  
A Priori Estimates ◽  
Mixed Boundary ◽  
A Priori ◽  
Mixed Boundary Conditions ◽  
Unit Interval ◽  
Priori Estimates ◽  
Sturm Liouville ◽  
Neumann Eigenvalues

We consider the Sturm–Liouville operator on the unit interval. We obtain two-sided a priori estimates of potential in terms of Dirichlet and Neumann eigenvalues and eigenvalues for 2 types of mixed boundary conditions.

Spectral analysis for the Sturm–Liouville operator on sun-type graphs

2011 ◽  
Vol 27 (9) ◽  
pp. 095003 ◽  
Author(s):  
Gerhard Freiling ◽  
Mikhail Ignatyev
Keyword(s):  
Spectral Analysis ◽  
Liouville Operator ◽  
Sturm Liouville
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