scholarly journals Eigenvalues of discrete linear second-order periodic and antiperiodic eigenvalue problems with sign-changing weight

2015 ◽  
Vol 467 ◽  
pp. 40-56 ◽  
Author(s):  
Chenghua Gao ◽  
Ruyun Ma
Keyword(s):  
Eigenvalue Problems ◽  
Second Order

Linear Second Order Eigenvalue Problems

2021 ◽  
pp. 283-348
Author(s):  
Svetlin G. Georgiev ◽  
Khaled Zennir
Keyword(s):  
Eigenvalue Problems ◽  
Second Order

Numerical methods for the solution of special and general sixth-order boundary-value problems, with applications to Bénard layer eigenvalue problems

1990 ◽  
Vol 431 (1883) ◽  
pp. 433-450 ◽  
Keyword(s):  
Numerical Methods ◽  
Boundary Value Problems ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Second Order ◽  
Sixth Order ◽  
Asymptotic Estimates ◽  
Eighth Order ◽  
The Family ◽  
Convergent Method

A family of numerical methods is developed for the solution of special nonlinear sixth-order boundary-value problems. Methods with second-, fourth-, sixth- and eighth-order convergence are contained in the family. The problem is also solved by writing the sixth-order differential equation as a system of three second-order differential equations. A family of second- and fourth-order convergent methods is then used to obtain the solution. A second-order convergent method is discussed for the numerical solution of general nonlinear sixth-order boundary-value problems. This method, with modifications where necessary, is applied to the sixth-order eigenvalue problems associated with the onset of instability in a Bénard layer. Numerical results are compared with asymptotic estimates appearing in the literature.

Full- and partial-range eigenfunction expansions for Sturm-Liouville problems with indefinite weights

1984 ◽  
Vol 98 (1-2) ◽  
pp. 69-88 ◽  
Author(s):  
Hans G. Kaper ◽  
Man Kam Kwong ◽  
C. G. Lekkerkerker ◽  
A. Zettl
Keyword(s):  
Hilbert Space ◽  
Differential Expression ◽  
Positive Operator ◽  
Eigenvalue Problems ◽  
Full Range ◽  
Second Order ◽  
Eigenfunction Expansions ◽  
Multiplicative Operator ◽  
Indefinite Weights ◽  
Sturm Liouville

SynopsisThis article is concerned with eigenvalue problems of the form Au = λTu in a Hilbert space H, where Ais a selfadjoint positive operator generated by a second-order Sturm-Liouville differential expression and T a selfadjoint indefinite multiplicative operator which is one-to-one. Emphasis is on the full-range and partial-range expansionproperties of the eigenfunctions.

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