Determination of leading coefficients in Sturm–Liouville operator from boundary measurements. I. A stripping algorithm

2002 ◽  
Vol 125 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Zahir Seyidmamedov ◽  
Alemdar Hasanov
Keyword(s):  
Liouville Operator ◽  
Boundary Measurements ◽  
Sturm Liouville

Determination of the impulsive Sturm–Liouville operator from a set of eigenvalues

2020 ◽  
Vol 28 (3) ◽  
pp. 341-348 ◽  
Author(s):  
Ran Zhang ◽  
Xiao-Chuan Xu ◽  
Chuan-Fu Yang ◽  
Natalia Pavlovna Bondarenko
Keyword(s):  
Boundary Conditions ◽  
Interior Point ◽  
Liouville Operator ◽  
Inverse Spectral Problem ◽  
Liouville Problem ◽  
Robin Boundary Conditions ◽  
Jump Conditions ◽  
Sturm Liouville ◽  
Robin Boundary

AbstractIn this work, we consider the inverse spectral problem for the impulsive Sturm–Liouville problem on {(0,\pi)} with the Robin boundary conditions and the jump conditions at the point {\frac{\pi}{2}}. We prove that the potential {M(x)} on the whole interval and the parameters in the boundary conditions and jump conditions can be determined from a set of eigenvalues for two cases: (i) the potential {M(x)} is given on {(0,\frac{(1+\alpha)\pi}{4})}; (ii) the potential {M(x)} is given on {(\frac{(1+\alpha)\pi}{4},\pi)}, where {0<\alpha<1}, respectively. It is also shown that the potential and all the parameters can be uniquely recovered by one spectrum and some information on the eigenfunctions at some interior point.

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