scholarly journals On integral representation for solution of generalized Sturm-Liouville equation with discontinuity conditions

2014 ◽  
Vol 33 (2) ◽  
pp. 97-109 ◽  
Author(s):  
Yalçın Güldü ◽  
Selma Gülyaz
Keyword(s):  
Integral Representation ◽  
Liouville Equation ◽  
Liouville Operator ◽  
Diffusion Potential ◽  
Half Line ◽  
Sturm Liouville ◽  
Discontinuity Conditions ◽  
Jost Solution

In this paper, some properties of kernel and integral representation of Jost solution are studied for Sturm-Liouville operator with diffusion potential and discontinuity on the half line.

scholarly journals Inverse problem for Sturm-Liouville operators on a curve

2019 ◽  
Vol 50 (3) ◽  
pp. 349-359
Author(s):  
Andrey Aleksandrovich Golubkov ◽  
Yulia Vladimirovna Kuryshova
Keyword(s):  
Inverse Problem ◽  
Asymptotic Behavior ◽  
Transfer Matrix ◽  
Liouville Equation ◽  
Inverse Spectral Problem ◽  
Rectifiable Curve ◽  
Uniqueness Of The Solution ◽  
Sturm Liouville ◽  
Discontinuity Conditions ◽  
Liouville Operators

he inverse spectral problem for the Sturm-Liouville equation with a piecewise-entire potential function and the discontinuity conditions for solutions on a rectifiable curve \(\gamma \subset \textbf{C}\) by the transfer matrix along this curve is studied. By the method of a unit transfer matrix the uniqueness of the solution to this problem is proved with the help of studying of the asymptotic behavior of the solutions to the Sturm-Liouville equation for large values of the spectral parameter module.

On the Friedrichs extension of semi-bounded difference operators

1994 ◽  
Vol 116 (1) ◽  
pp. 167-177 ◽  
Author(s):  
M. Benammar ◽  
W. D. Evans
Keyword(s):  
Liouville Equation ◽  
Liouville Operator ◽  
Difference Operators ◽  
Dirichlet Integral ◽  
Friedrichs Extension ◽  
Sturm Liouville

In [5] Kalf obtained a characterization of the Friedrichs extension TF of a general semi-bounded Sturm–Liouville operator T, the only assumptions made on the coefficients being those necessary for T to be defined. The domain D(TF) of TF was described in terms of ‘weighted’ Dirichiet integrals involving the principal and non-principal solutions of an associated non-oscillatory Sturm–Liouville equation. Conditions which ensure that members of D(TF) have a finite Dirichlet integral were subsequently given by Rosenberger in [7].

scholarly journals Inverse spectral-scattering problem for the Sturm-Liouville operator on a noncompact star-type graph

2013 ◽  
Vol 44 (3) ◽  
pp. 327-349 ◽  
Author(s):  
Sergey Buterin ◽  
G. Freiling
Keyword(s):  
Finite Number ◽  
Spectral Data ◽  
Liouville Operator ◽  
Scattering Problem ◽  
Internal Vertex ◽  
Scattering Data ◽  
Half Line ◽  
Matching Conditions ◽  
Method Of Spectral Mappings ◽  
Sturm Liouville

We study the Sturm-Liouville operator on a noncompact star-type graph consisting of a finite number of compact and noncompact edges under standard matching conditions in the internal vertex. We introduce and investigate the so-called spectral-scat\-tering data, which generalize the classical spectral data for the Sturm-Liouville operator on the half-line and the scattering data on the line. Developing the idea of the method of spectral mappings we prove that the specification of the spectral-scattering data uniquely determines the Sturm-Liouville operator on the graph.

Sign in / Sign up

Export Citation Format

Share Document