On the scattering problem for the sturm-liouville equation on the half line with sign valued weight coefficient

1995 ◽  
Vol 57 (3-4) ◽  
pp. 333-339 ◽  
Author(s):  
Zaki F. Abd-El-Reheem
Keyword(s):  
Liouville Equation ◽  
Scattering Problem ◽  
Weight Coefficient ◽  
Half Line ◽  
Sturm Liouville

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.

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.

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