Spectral properties of the Sturm-Liouville operator with a parameter that changes sign and their usage to the study of the spectrum of differential operators of mathematical physics belonging to different types

2018 ◽  
Author(s):  
Mussakan B. Muratbekov ◽  
Madi M. Muratbekov
Keyword(s):  
Liouville Operator ◽  
Spectral Properties ◽  
Differential Operators ◽  
Mathematical Physics ◽  
Different Types ◽  
Sturm Liouville

Inverse nodal problems for integro-differential operators with a constant delay

2019 ◽  
Vol 27 (4) ◽  
pp. 501-509 ◽  
Author(s):  
Murat Sat ◽  
Chung Tsun Shieh
Keyword(s):  
Integral Operator ◽  
Potential Function ◽  
Liouville Operator ◽  
Differential Operators ◽  
Constant Delay ◽  
Nodal Points ◽  
Inverse Nodal Problems ◽  
Volterra Integral Operator ◽  
Sturm Liouville

Abstract We study inverse nodal problems for Sturm–Liouville operator perturbed by a Volterra integral operator with a constant delay. We have estimated nodal points and nodal lengths for this operator. Moreover, by using these data, we have shown that the potential function of this operator can be established uniquely.

Spectral Properties of a q-Sturm–Liouville Operator

2008 ◽  
Vol 287 (1) ◽  
pp. 259-274 ◽  
Author(s):  
B. Malcolm Brown ◽  
Jacob S. Christiansen ◽  
Karl Michael Schmidt
Keyword(s):  
Liouville Operator ◽  
Spectral Properties ◽  
Sturm Liouville

scholarly journals Fundamental Spectral Theory of Fractional Singular Sturm-Liouville Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Erdal Bas
Keyword(s):  
Spectral Theory ◽  
Liouville Operator ◽  
Spectral Properties ◽  
Liouville Problem ◽  
Eigenvalues And Eigenfunctions ◽  
Sturm Liouville

We give the theory of spectral properties for eigenvalues and eigenfunctions of Bessel type of fractional singular Sturm-Liouville problem. We show that the eigenvalues and eigenfunctions of the problem are real and orthogonal, respectively. Furthermore, we prove new approximations about the topic.

On Schrödinger's factorization method for Sturm-Liouville operators

1978 ◽  
Vol 80 (1-2) ◽  
pp. 67-84 ◽  
Author(s):  
U.-W. Schmincke
Keyword(s):  
Discrete Spectrum ◽  
Liouville Operator ◽  
Differential Operators ◽  
Factorization Method ◽  
Friedrichs Extension ◽  
First Order ◽  
Sturm Liouville ◽  
Image Position ◽  
Special Case ◽  
Liouville Operators

SynopsisWe consider the Friedrichs extension A of a minimal Sturm-Liouville operator L0 and show that A admits a Schrödinger factorization, i.e. that one can find first order differential operators Bk with where the μk are suitable numbers which optimally chosen are just the lower eigenvalues of A (if any exist). With the help of this theorem we derive for the special case L0u = −u″ + q(x)u with q(x) → 0 (|x| → ∞) the inequalityσd(A) being the discrete spectrum of A. This inequality is seen to be sharp to some extent.

Inverse problems on star-type graphs: differential operators of different orders on different edges

2014 ◽  
Vol 12 (3) ◽  
Author(s):  
Vyacheslav Yurko
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Liouville Operator ◽  
Differential Operators ◽  
Compact Star ◽  
Spectral Characteristics ◽  
Weyl Function ◽  
Inverse Spectral Problems ◽  
Sturm Liouville

AbstractWe study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.

scholarly journals Spectral properties of an impulsive Sturm–Liouville operator

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Elgiz Bairamov ◽  
Ibrahim Erdal ◽  
Seyhmus Yardimci
Keyword(s):  
Liouville Operator ◽  
Spectral Properties ◽  
Sturm Liouville
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