Some questions in spectral theory for the operator Sturm-Liouville equation on the half-line

1985 ◽  
pp. 5-18
Author(s):  
M. L. Gorbachuk ◽  
V. A. Kutovoĭ
Keyword(s):  
Spectral Theory ◽  
Liouville Equation ◽  
Half Line ◽  
Sturm Liouville

scholarly journals An application of comparison criteria to fractional spectral problem having Coloumb potential

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 79-85 ◽  
Author(s):  
Erdal Bas ◽  
Turk Metin
Keyword(s):  
Boundary Condition ◽  
Spectral Problem ◽  
Spectral Theory ◽  
Liouville Equation ◽  
Coulomb Potential ◽  
Liouville Problem ◽  
Comparison Theorems ◽  
Liouville Theory ◽  
Sturm Liouville ◽  
Comparison Criteria

In this study, the zeros of eigen functions of spectral theory are considered in fractional Sturm-Liouville problem. The 1st and 2nd comparison theorems for fractional Sturm-Liouville equation with boundary condition and their proofs are given. In this way, our new approximation will contribute to construct fractional Sturm-Liouville theory. Also, its an application is given in case of Coulomb potential and the results are presented by a symbolic graph.

scholarly journals On integral representation for solution of generalized Sturm-Liouville equation with discontinuity conditions

2014 ◽  
Vol 33 (2) ◽  
pp. 97-109 ◽  
Author(s):  
Yalçın Güldü ◽  
Selma Gülyaz
Keyword(s):  
Integral Representation ◽  
Liouville Equation ◽  
Liouville Operator ◽  
Diffusion Potential ◽  
Half Line ◽  
Sturm Liouville ◽  
Discontinuity Conditions ◽  
Jost Solution

In this paper, some properties of kernel and integral representation of Jost solution are studied for Sturm-Liouville operator with diffusion potential and discontinuity on the half line.

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.

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