The canonical product of the solution of the Sturm-Liouville equation in one turning point case

2000 ◽  
Vol 8 (4) ◽  
pp. 305-320 ◽  
Author(s):  
A. Jodayree Akbarfam ◽  
A. Mingarelli
Keyword(s):  
Liouville Equation ◽  
Turning Point ◽  
Canonical Product ◽  
Sturm Liouville

On the Canonical Solution of the Sturm–Liouville Problem with Singularity and Turning Point of Even Order

2011 ◽  
Vol 54 (3) ◽  
pp. 506-518 ◽  
Author(s):  
A. Neamaty ◽  
S. Mosazadeh
Keyword(s):  
Liouville Equation ◽  
Turning Point ◽  
Infinite Product ◽  
Liouville Problem ◽  
Asymptotic Estimates ◽  
Product Representation ◽  
Representation Of Solutions ◽  
Even Order ◽  
Sturm Liouville ◽  
Infinite Product Representation

AbstractIn this paper, we are going to investigate the canonical property of solutions of systems of differential equations having a singularity and turning point of even order. First, by a replacement, we transform the system to the Sturm–Liouville equation with turning point. Using of the asymptotic estimates provided by Eberhard, Freiling, and Schneider for a special fundamental system of solutions of the Sturm–Liouville equation, we study the infinite product representation of solutions of the systems. Then we transform the Sturm–Liouville equation with turning point to the equation with singularity, then we study the asymptotic behavior of its solutions. Such representations are relevant to the inverse spectral problem.

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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