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

scholarly journals Spectral analysis of singular Sturm-Liouville operators on time scales

2018 ◽  
Vol 72 (1) ◽  
pp. 1 ◽  
Author(s):  
Bilender P. Allahverdiev ◽  
Huseyin Tuna
Keyword(s):  
Spectral Analysis ◽  
Continuous Spectrum ◽  
Discrete Spectrum ◽  
Time Scales ◽  
Liouville Operator ◽  
Adjoint Operator ◽  
The Self ◽  
Sturm Liouville ◽  
Liouville Operators

In this paper, we consider properties of the spectrum of a Sturm-Liouville<br />operator on time scales. We will prove that the regular symmetric<br />Sturm-Liouville operator is semi-bounded from below. We will also give some<br />conditions for the self-adjoint operator associated with the singular<br />Sturm-Liouville expression to have a discrete spectrum. Finally, we will<br />investigate the continuous spectrum of this operator.

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}.

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