Asymptotic linearity and a class of noninear Sturm-Liouville problems on the half line

1974 ◽  
pp. 429-433
Author(s):  
J. F. Toland
Keyword(s):  
Half Line ◽  
Sturm Liouville ◽  
Asymptotic Linearity

scholarly journals On Povzner–Wienholtz-type self-adjointness results for matrix-valued Sturm–Liouville operators

2003 ◽  
Vol 133 (4) ◽  
pp. 747-758 ◽  
Author(s):  
Steve Clark ◽  
Fritz Gesztesy
Keyword(s):  
Half Line ◽  
Sturm Liouville ◽  
Image Position ◽  
Liouville Operators

We derive Povzner–Wienholtz-type self-adjointness results for m × m matrix-valued Sturm–Liouville operators in L2((a, b);R dx)m, m ∈ N, for (a, b) a half-line or R.

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 Description of the scattering data for Sturm-Liouville operators on the half-line

2019 ◽  
Vol 39 (4) ◽  
pp. 557-576
Author(s):  
Yaroslav Mykytyuk ◽  
Nataliia Sushchyk
Keyword(s):  
Nondecreasing Function ◽  
Scattering Data ◽  
Half Line ◽  
Sturm Liouville ◽  
Liouville Operators

We describe the set of the scattering data for self-adjoint Sturm-Liouville operators on the half-line with potentials belonging to \(L_1(\mathbb{R}_+,\rho(x)\,\text{d} x)\), where \(\rho:\mathbb{R}_+\to\mathbb{R}_+\) is a monotonically nondecreasing function from some family \(\mathscr{R}\). In particular, \(\mathscr{R}\) includes the functions \(\rho(x)=(1+x)^{\alpha}\) with \(\alpha\geq 1\).

An inverse problem for Sturm–Liouville operators on the half-line with complex weights

2019 ◽  
Vol 27 (3) ◽  
pp. 439-443
Author(s):  
Vjacheslav Yurko
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Operators ◽  
Spectral Characteristics ◽  
Half Line ◽  
Sturm Liouville ◽  
The Given ◽  
Complex Valued ◽  
The Uniqueness Theorem ◽  
Liouville Operators

Abstract Second order differential operators on the half-line with complex-valued weights are considered. Properties of spectral characteristics are established, and the inverse problem of recovering operator’s coefficients from the given Weyl-type function is studied. The uniqueness theorem is proved for this class of nonlinear inverse problems, and a number of examples are provided.

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