Inverse transmission eigenvalue problems with the twin-dense nodal subset

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.

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

Mathematical Modelling and Analysis ◽

10.3846/1392-6292.2010.15.383-392 ◽

2010 ◽

Vol 15 (3) ◽

pp. 383-392 ◽

Cited By ~ 1

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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Dissipative eigenvalue problems for a Sturm–Liouville operator with a singular potential

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500000664 ◽

2000 ◽

Vol 130 (6) ◽

pp. 1237-1257 ◽

Cited By ~ 6

Author(s):

Bernhard Bodenstorfer ◽

Aad Dijksma ◽

Heinz Langer

Keyword(s):

Liouville Operator ◽

Eigenvalue Problems ◽

Dirichlet Condition ◽

Continuous Functions ◽

Dirichlet Boundary Conditions ◽

Interface Condition ◽

Associated Functions ◽

Sturm Liouville ◽

Bari Basis ◽

Symmetric Operators

In this paper we consider the Sturm–Liouville operator d2/dx2 − 1/x on the interval [a, b], a < 0 < b, with Dirichlet boundary conditions at a and b, for which x = 0 is a singular point. In the two components L2(a, 0) and L2(0, b) of the space L2(a, b) = L2(a, 0) ⊕ L2(0, b) we define minimal symmetric operators and describe all the maximal dissipative and self-adjoint extensions of their orthogonal sum in L2(a, b) by interface conditions at x = 0. We prove that the maximal dissipative extensions whose domain contains only continuous functions f are characterized by the interface condition limx→0+(f′(x)−f′(−x)) = γf(0) with γ∈C+∪R or by the Dirichlet condition f(0+) = f(0−) = 0. We also show that the corresponding operators can be obtained by norm resolvent approximation from operators where the potential 1/x is replaced by a continuous function, and that their eigen and associated functions can be chosen to form a Bari basis in L2(a, b).

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

Boundary Value Problems ◽

10.1186/s13661-014-0222-3 ◽

2014 ◽

Vol 2014 (1) ◽

Author(s):

Hikmet Koyunbakan

Keyword(s):

Liouville Equation ◽

Inverse Nodal Problem ◽

Laplacian Energy ◽

Sturm Liouville ◽

Nodal Problem ◽

Energy Dependent

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