The Reconstruction of the Attracting Potential in the Sturm-Liouville Equation through Characteristics of Negative Discrete Spectrum

1996 ◽  
Vol 97 (1) ◽  
pp. 19-52 ◽  
Author(s):  
G. M. Henkin ◽  
N. N. Novikova
Keyword(s):  
Discrete Spectrum ◽  
Liouville Equation ◽  
Sturm Liouville

scholarly journals On partial fractional Sturm–Liouville equation and inclusion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zohreh Zeinalabedini Charandabi ◽  
Hakimeh Mohammadi ◽  
Shahram Rezapour ◽  
Hashem Parvaneh Masiha
Keyword(s):  
Differential Equation ◽  
Liouville Equation ◽  
Existence Of Solutions ◽  
Liouville Problem ◽  
Existence Of A Solution ◽  
Contractive Mappings ◽  
Sturm Liouville

AbstractThe Sturm–Liouville differential equation is one of interesting problems which has been studied by researchers during recent decades. We study the existence of a solution for partial fractional Sturm–Liouville equation by using the α-ψ-contractive mappings. Also, we give an illustrative example. By using the α-ψ-multifunctions, we prove the existence of solutions for inclusion version of the partial fractional Sturm–Liouville problem. Finally by providing another example and some figures, we try to illustrate the related inclusion result.

Sturm-Liouville operators with an indefinite weight function

1977 ◽  
Vol 78 (1-2) ◽  
pp. 161-191 ◽  
Author(s):  
K. Daho ◽  
H. Langer
Keyword(s):  
Weight Function ◽  
Liouville Equation ◽  
Spectral Properties ◽  
Scalar Product ◽  
Main Tool ◽  
Indefinite Weight ◽  
Indefinite Weight Function ◽  
Sturm Liouville ◽  
Liouville Operators

SynopsisSpectral properties of the singular Sturm-Liouville equation –(p−1y′)′ + qy = λry with an indefinite weight function r are studied in . The main tool is the theory of definitisable operators in spaces with an indefinite scalar product.

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