scholarly journals Inverse spectral problem for Sturm-Liouville operator with discontinuous coefficient and cubic polynomials of spectral parameter in boundary condition

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Aynur Çöl
Keyword(s):  
Boundary Condition ◽  
Spectral Problem ◽  
Spectral Parameter ◽  
Liouville Operator ◽  
Inverse Spectral Problem ◽  
Discontinuous Coefficient ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Cubic Polynomials

scholarly journals An Inverse Spectral Problem for the Sturm-Liouville Operator on a Three-Star Graph

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
I. Dehghani Tazehkand ◽  
A. Jodayree Akbarfam
Keyword(s):  
Inverse Problem ◽  
Spectral Problem ◽  
Liouville Operator ◽  
Inverse Spectral Problem ◽  
Spectral Characteristics ◽  
Star Graph ◽  
Dirichlet Problems ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
Robin Boundary

We study an inverse spectral problem for the Sturm-Liouville operator on a three-star graph with the Dirichlet and Robin boundary conditions in the boundary vertices and matching conditions in the internal vertex. As spectral characteristics,we consider the spectrum of the main problem together with the spectra of two Dirichlet-Dirichlet problems and one Robin-Dirichlet problem on the edges of the graph and investigate their properties and asymptotic behavior. We prove that if these four spectra do not intersect, then the inverse problem of recovering the operator is uniquely solvable.We give an algorithm for the solution of the inverse problem with respect to this quadruple of spectra.

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