scholarly journals Equivalence of Sturm-Liouville Problem with Finitely Many δ-Interactions and Matrix Eigenvalue Problems

2018 ◽  
Keyword(s):  
Eigenvalue Problems ◽  
Liouville Problem ◽  
Matrix Eigenvalue ◽  
Sturm Liouville ◽  
Matrix Eigenvalue Problems

scholarly journals Some Modified Matrix Eigenvalue Problems

SIAM Review ◽  
1973 ◽  
Vol 15 (2) ◽  
pp. 318-334 ◽  
Author(s):  
Gene H. Golub
Keyword(s):  
Eigenvalue Problems ◽  
Matrix Eigenvalue ◽  
Matrix Eigenvalue Problems

scholarly journals The dual eigenvalue problems of the conformable fractional Sturm–Liouville problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yan-Hsiou Cheng
Keyword(s):  
Eigenvalue Problems ◽  
Liouville Problem ◽  
First Eigenvalue ◽  
Liouville Property ◽  
The First Eigenvalue ◽  
Eigenvalue Gap ◽  
Single Well ◽  
Eigenvalue Ratio ◽  
Sturm Liouville ◽  
Prüfer Substitution

AbstractIn this paper, we are concerned with the eigenvalue gap and eigenvalue ratio of the Dirichlet conformable fractional Sturm–Liouville problems. We show that this kind of differential equation satisfies the Sturm–Liouville property by the Prüfer substitution. That is, the nth eigenfunction has $n-1$ n − 1 zero in $( 0,\pi ) $ ( 0 , π ) for $n\in \mathbb{N}$ n ∈ N . Then, using the homotopy argument, we find the minimum of the first eigenvalue gap under the class of single-well potential functions and the first eigenvalue ratio under the class of single-barrier density functions. The result of the eigenvalue gap is different from the classical Sturm–Liouville problem.

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