scholarly journals Erratum: Inverse nodal problem for p-Laplacian energy-dependent Sturm-Liouville equation

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Hikmet Koyunbakan
Keyword(s):  
Liouville Equation ◽  
Inverse Nodal Problem ◽  
Laplacian Energy ◽  
Sturm Liouville ◽  
Nodal Problem ◽  
Energy Dependent

scholarly journals Inverse nodal problem for p−Laplacian Bessel equation with polynomially dependent spectral parameter

2018 ◽  
Vol 51 (1) ◽  
pp. 255-263
Author(s):  
Emrah Yilmaz ◽  
Mudhafar Hamadamen ◽  
Tuba Gulsen
Keyword(s):  
Boundary Condition ◽  
Liouville Equation ◽  
Reconstruction Formula ◽  
Bessel Equation ◽  
Inverse Nodal Problem ◽  
Laplacian Energy ◽  
Sturm Liouville ◽  
Nodal Problem ◽  
Energy Dependent ◽  
Prüfer Substitution

Abstract In this study, solution of inverse nodal problem for p−Laplacian Bessel equation is extended to the case that boundary condition depends on polynomial eigenparameter. To find spectral datas as eigenvalues and nodal parameters of this problem, we used a modified Prüfer substitution. Then, reconstruction formula of the potential functions is also obtained by using nodal lenghts. However, this method is similar to used in [Koyunbakan H., Inverse nodal problem for p−Laplacian energy-dependent Sturm-Liouville equation, Bound. Value Probl., 2013, 2013:272, 1-8], our results are more general.

Inverse transmission eigenvalue problems with the twin-dense nodal subset

2017 ◽  
Vol 25 (2) ◽  
Author(s):  
Yu Ping Wang ◽  
Chung Tsun Shieh ◽  
Hong Yi Miao
Keyword(s):  
Liouville Operator ◽  
Eigenvalue Problems ◽  
Inverse Nodal Problem ◽  
Transmission Eigenvalue ◽  
Sturm Liouville ◽  
Nodal Problem

Abstract The inverse nodal problem for the Sturm-Liouville operator

Inverse nodal problem for polynomial pencil of Sturm‐Liouville operator

2018 ◽  
Vol 41 (17) ◽  
pp. 7576-7582 ◽  
Author(s):  
Sertac Goktas ◽  
Hikmet Koyunbakan ◽  
Tuba Gulsen
Keyword(s):  
Liouville Operator ◽  
Inverse Nodal Problem ◽  
Sturm Liouville ◽  
Nodal Problem

scholarly journals Numerical investigation of the inverse nodal problem by Chebisyhev interpolation method

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 123-136 ◽  
Author(s):  
Tuba Gulsen ◽  
Emrah Yilmaz ◽  
Shahrbanoo Akbarpoor
Keyword(s):  
Boundary Data ◽  
Interpolation Method ◽  
Approximate Solutions ◽  
Jump Conditions ◽  
Numerical Examples ◽  
Inverse Nodal Problem ◽  
Chebyshev Interpolation ◽  
Sturm Liouville ◽  
Nodal Problem ◽  
The Stability

In this study, we deal with the inverse nodal problem for Sturm-Liouville equation with eigenparameter-dependent and jump conditions. Firstly, we obtain reconstruction formulas for potential function, q, under a condition and boundary data, ?, as a limit by using nodal points to apply the Chebyshev interpolation method. Then, we prove the stability of this problem. Finally, we calculate approximate solutions of the inverse nodal problem by considering the Chebyshev interpolation method. We then present some numerical examples using Matlab software program to compare the results obtained by the classical approach and by Chebyshev polynomials for the solutions of the problem.

scholarly journals INVERSE NODAL PROBLEM FOR A CLASS OF NONLOCAL STURM‐LIOUVILLE OPERATOR

2010 ◽  
Vol 15 (3) ◽  
pp. 383-392 ◽  
Author(s):  
Chuan-Fu Yang
Keyword(s):  
Boundary Condition ◽  
Dense Subset ◽  
Liouville Problem ◽  
Integral Boundary ◽  
Inverse Nodal Problem ◽  
Classical Boundary Condition ◽  
Classical Boundary ◽  
Sturm Liouville ◽  
Nodal Problem ◽  
The Given

Inverse nodal problem consists in constructing operators from the given nodes (zeros) of their eigenfunctions. In this work, the Sturm‐Liouville problem with one classical boundary condition and another nonlocal integral boundary condition is considered. We prove that a dense subset of nodal points uniquely determine the boundary condition parameter and the potential function of the Sturm‐Liouville equation. We also provide a constructive procedure for the solution of the inverse nodal problem.

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